Reflection of Light - Questions & Answers

EXERCISE-7(A)

(A) MULTIPLE CHOICE TYPE :
(Choose the correct answer from the options given below).

1. The angle which the ........... ray makes with the ........ at the point of incidence is called angle of incidence.
(a) reflected, mirror (b) incidence, mirror
(c) incidence, normal (d) reflected, normal
Step 1: The angle of incidence is formed by the incoming light ray.
Step 2: This angle is always measured from an imaginary perpendicular line called the normal.
Answer: The angle which the incidence ray makes with the normal at the point of incidence is called angle of incidence. Correct option: (c)

2. Regular reflection occurs when a beam of light falls on a ..............
(a) smooth surface (b) polished surface
(c) rough surface (d) Both (a) and (b)
Step 1: Regular reflection means the reflected rays remain parallel to each other.
Step 2: This requires a surface with no irregularities, which is both smooth and polished.
Answer: Regular reflection occurs when a beam of light falls on a smooth surface / polished surface. Correct option: (d) Both (a) and (b)

3. According to the law of reflection :
(a) i/r = constant (b) sin i/sin r = constant
(c) i + r = constant (d) i = r
Step 1: The first law of reflection states that the angle the light hits the mirror is the same as the angle it bounces off.
Step 2: Therefore, angle of incidence (i) equals angle of reflection (r).
Answer: (d) i = r

4. The image formed due to the actual intersection of the reflected rays is :
(a) virtual (b) diminished
(c) real (d) enlarged
Step 1: When light rays physically cross each other after reflecting, they form an image on a screen.
Step 2: Images that can be captured on a screen are called real images.
Answer: (c) real

5. The image formed by a plane mirror is :
(a) erect and diminished (b) erect and enlarged
(c) inverted and of same size (d) erect and of same size.
Step 1: When you look in a flat mirror, you appear right-side up (erect).
Step 2: Your reflection also appears to be exactly your height (same size).
Answer: (d) erect and of same size

6. The image formed by a plane mirror is :
(a) real (b) virtual
(c) virtual with lateral inversion (d) real with lateral inversion.
Step 1: Plane mirrors form images behind the mirror where light doesn't actually go, so they are virtual.
Step 2: Your left side appears on the right in the mirror, which is called lateral inversion.
Answer: (c) virtual with lateral inversion

7. A concave mirror forms ........... image whereas a convex mirror forms ........... .
(a) real, real (b) virtual, real
(c) virtual, virtual (d) real, virtual
Step 1: A concave mirror can focus light to a point, forming a real image.
Step 2: A convex mirror always spreads light out, forming a virtual image behind the mirror.
Answer: A concave mirror forms real image whereas a convex mirror forms virtual. Correct option: (d) real, virtual

8. Which of the following combination of letters does not show lateral inversion ?
(a) A, C, I (b) M, T, V
(c) D, L, A (d) X, Y, Z
Step 1: Lateral inversion is unnoticeable in letters that look identical when flipped left-to-right (symmetrical).
Step 2: Letters M, T, and V are perfectly symmetrical down the middle.
Answer: (b) M, T, V

9. If an object is shifted by a distance d towards a plane mirror, the image will shift by distance ........... towards the mirror.
(a) d (b) 2d
(c) 4d (d) None of the above
Step 1: In a plane mirror, the image is always at the exact same distance behind the mirror as the object is in front.
Step 2: If the object moves forward by 'd', the image must also move forward by 'd' to maintain this equal distance.
Answer: If an object is shifted by a distance d towards a plane mirror, the image will shift by distance d towards the mirror. Correct option: (a) d

(B) VERY SHORT ANSWER TYPE :

1. Select the luminous object(s) from the following :
Sun, Moon, Earth, Shooting star, Fire
Step 1: Luminous objects are those that generate and emit their own light.
Step 2: The Sun, a shooting star (due to friction/heat), and fire generate their own light, while the Moon and Earth only reflect it.
Answer: Sun, Shooting star, Fire

2. What do you mean by reflection of light ?
Step 1: Think about what happens when light hits an obstacle it cannot pass through.
Step 2: The light bounces back into the same space it came from.
Answer: The return of light into the same medium after striking a surface is called reflection.

3. State which surface of a plane mirror reflects most of the light incident on it : the front smooth surface or the back silvered surface.
Step 1: A plane mirror consists of a glass sheet with a coating on the back.
Step 2: While the glass reflects a little bit of light, the thick metal (silver) coating on the back does almost all the reflecting.
Answer: The back silvered surface.

4. A light ray is incident normally on a plane mirror.
(a) What is its angle of incidence ?
(b) What is the direction of reflected ray ? Show it on a diagram.
Step 1: "Normally" means hitting the mirror straight on, right along the 90-degree normal line.
Step 2: Since it is on the normal line, the angle between the ray and the normal is zero.
Step 3: By the law of reflection, if incidence is zero, reflection is also zero, so it bounces straight back.
Answer: (a) 0° (b) It retraces its path in the opposite direction. (Diagram: Draw a single straight line meeting the mirror at 90°, with arrows pointing both down towards the mirror and up away from it).

5. For a ray reflected on a plane mirror, find the ratio of sin i/sin r.
Step 1: The law of reflection states that angle i = angle r.
Step 2: Because the angles are identical, their sine values (sin i and sin r) must also be identical.
Step 3: Dividing a number by the exact same number gives 1.
Answer: 1

6. Light from a torch is reflected by a white sheet of paper and a black polished mica sheet. Which of the two will produce a stronger reflected beam ?
Step 1: A white sheet of paper has a rough surface, causing irregular reflection (scattering light everywhere).
Step 2: A polished mica sheet is smooth and shiny, causing regular reflection (keeping the beam strong and focused).
Answer: Black polished mica sheet.

7. A light ray strikes a mirror and retraces its path. What is the angle of incidence and angle of reflection ?
Step 1: If a ray bounces straight back along its original path, it means it hit the mirror at exactly 90 degrees to the surface.
Step 2: This path is the normal line, so the angle to the normal is 0.
Step 3: Both incidence and reflection angles are zero.
Answer: Angle of incidence = 0°, Angle of reflection = 0°.

(C) SHORT ANSWER TYPE :

1. Explain the following terms :
(a) plane mirror, (b) incident ray,
(c) reflected ray, (d) angle of incidence, and
(e) angle of reflection.
Draw diagram/diagrams to show them.
Step 1: Define a plane mirror as a flat reflective surface.
Step 2: The incident ray is the incoming light, and the reflected ray is the outgoing light.
Step 3: The angles are measured between these rays and the perpendicular normal line.
Answer:
(a) Plane mirror: A highly polished, flat surface that reflects light regularly.
(b) Incident ray: The light ray striking a reflecting surface.
(c) Reflected ray: The light ray obtained after reflection from the surface.
(d) Angle of incidence: The angle between the incident ray and the normal.
(e) Angle of reflection: The angle between the reflected ray and the normal.
(Diagram: Draw a flat line for the mirror, a dashed normal line perpendicular to it, an incoming ray forming angle 'i', and an outgoing ray forming angle 'r').

2. Differentiate between reflection of light from a plane mirror and that from a plane wall.
Step 1: Consider the microscopic texture of the surfaces.
Step 2: A mirror is smooth and reflects light parallelly (regular).
Step 3: A wall is rough and scatters light in all directions (irregular).
Answer: A plane mirror causes regular reflection (a parallel beam remains parallel), whereas a plane wall causes irregular or diffused reflection (rays scatter in different directions).

3. State the two laws of reflection of light.
Step 1: State the relationship between the angles.
Step 2: State the geometric relationship of the rays and the normal.
Answer: 1. The angle of incidence is equal to the angle of reflection (i = r). 2. The incident ray, the reflected ray, and the normal at the point of incidence, all lie in the same plane.

4. Draw a diagram to show the reflection of a ray of light by a plane mirror. In the diagram, label the incident ray, the reflected ray, the normal, the angle of incidence and the angle of reflection.
Step 1: Start with a horizontal line with shading below to represent the mirror.
Step 2: Draw a perpendicular dashed line in the center for the normal.
Step 3: Draw an incoming ray and an outgoing ray on opposite sides of the normal, labeling all parts clearly.
Answer: (Draw a straight horizontal line for the mirror with diagonal shading underneath. Draw a perpendicular dashed line called the normal. Draw an incoming ray labeled "Incident Ray" making angle i with the normal, and an outgoing ray labeled "Reflected Ray" making angle r with the normal).

5. Differentiate between a real and a virtual image.
Step 1: Think about how the light rays behave after reflecting.
Step 2: If they physically cross, the image is real. If they only appear to cross behind the mirror, the image is virtual.
Answer: A real image is formed by the actual intersection of reflected rays, is always inverted, and can be obtained on a screen. A virtual image is formed when rays only appear to diverge from a point, is always erect, and cannot be obtained on a screen.

6. What is meant by lateral inversion of an image in a plane mirror ? Explain it with the help of a ray diagram.
Step 1: Define how the left and right sides swap in a mirror reflection.
Step 2: Describe drawing an asymmetrical object (like a letter) and tracing rays to show its flipped image.
Answer: The interchange of the left and right sides in the image of an object formed by a plane mirror is called lateral inversion. (Ray diagram: Draw a letter like 'P' in front of a plane mirror. Trace incident and reflected rays from its key points to show the virtual image appears flipped as 'q').

7. The letters on the front of an ambulance are written laterally inverted like ECNALUBMA. Give reason.
Step 1: Vehicles have rear-view mirrors which are plane or convex mirrors.
Step 2: These mirrors cause lateral inversion (flipping left and right).
Step 3: If written backward on the ambulance, the mirror flips it again, making it readable.
Answer: Because of lateral inversion in plane mirrors, the driver of a vehicle moving ahead can read the word correctly as "AMBULANCE" in their rear-view mirror and give way to it quickly.

(D) LONG ANSWER TYPE :

1. With the help of diagrams, explain the difference between regular and irregular reflection.
Step 1: Define regular reflection as light hitting a smooth surface and reflecting neatly.
Step 2: Define irregular reflection as light hitting a rough surface and scattering.
Step 3: Draw diagrams illustrating both.
Answer: Regular reflection occurs when a parallel beam of light falls on a smooth surface and reflects as a parallel beam in a fixed direction. Irregular reflection occurs when light falls on a rough surface and reflects in different directions, letting us see objects from any angle. (Diagrams: For regular, draw parallel incoming rays reflecting as parallel outgoing rays. For irregular, draw parallel incoming rays reflecting in many scattered angles off a bumpy line).

2. State the laws of reflection and describe an experiment to verify them.
Step 1: Write down the two laws of reflection.
Step 2: Describe the standard pin experiment on a drawing board to prove the angles are equal and all lines lie on the flat paper.
Answer: Laws: (i) Angle of incidence = angle of reflection. (ii) Incident ray, normal, and reflected ray lie in the same plane. Experiment: Fix a paper on a drawing board, place a plane mirror vertically. Draw a normal line and an incident line at an angle. Place two pins vertically on the incident line. Look into the mirror from the other side and place two more pins so they align perfectly with the mirror images of the first two pins. Draw a line through these new pins for the reflected ray. Measure the angles with a protractor to find i = r, verifying the first law. Because all pins and lines lie perfectly flat on the paper, the second law is verified.

3. Fig. 7.15 shows an incident ray AO and the normal ON on a plane mirror. The angle which the incident ray AO makes with the mirror is 30°. (a) Find the angle of incidence. (b) Draw the reflected ray and then find the angle between the incident and reflected rays.
Step 1: The normal makes a 90° angle with the mirror.
Step 2: If the ray makes 30° with the mirror, the angle of incidence (with the normal) is 90° - 30° = 60°.
Step 3: By law of reflection, angle of reflection is also 60°.
Step 4: Total angle is 60° + 60° = 120°.
Answer: (a) Angle of incidence i = 90° - 30° = 60°. (b) Angle of reflection r = 60°. The total angle between the incident and reflected rays = i + r = 60° + 60° = 120°.

4. The diagram in Fig. 7.16 shows a point object P in front of a plane mirror MM1.
(a) Complete the diagram by taking two rays from the point P to show the formation of its image.
(b) In the diagram, mark the position of eye to see the image.
(c) Is the image formed real or virtual ? Explain why ?
Step 1: Draw two rays spreading out from P and hitting the mirror.
Step 2: Reflect them back. To find the image, extend the reflected lines straight back behind the mirror.
Step 3: The eye must be placed where the reflected rays go.
Step 4: Since light doesn't actually go behind the mirror, the image is virtual.
Answer: (a) Draw two diverging rays from P to the mirror, reflect them obeying the laws of reflection, and extend the reflected rays backward (as dashed lines) to meet at image point P'. (b) Draw an eye symbol on the side of the reflected rays to receive the light. (c) The image is virtual, because the reflected rays do not actually intersect but only appear to meet when produced backwards.

5. The diagram below in Fig. 7.17 shows an object XY in front of a plane mirror MM1. Draw on the diagram, path of two rays from each point X and Y of the object to show the formation of its image.
Step 1: Treat top point X and bottom point Y as separate objects.
Step 2: Draw two incident and reflected rays for X, extending backward to find virtual point X'.
Step 3: Do the same for point Y to find virtual point Y'.
Step 4: Connect X' and Y' to form the full virtual image.
Answer: (Draw two incident rays from point X to the mirror, reflect them, and extend backward with dashed lines to form X'. Repeat this exact process with two rays for point Y to form Y'. Draw a dotted line connecting X' and Y' to show the complete virtual image).

(E) NUMERICALS :

1. A ray is incident on a plane mirror. Its reflected ray is perpendicular to the incident ray. Find the angle of incidence.
Step 1: Perpendicular means the total angle between the incident and reflected ray is 90°.
Step 2: This total angle is the sum of angle of incidence (i) and angle of reflection (r). So, i + r = 90°.
Step 3: Since i = r (law of reflection), we can write 2i = 90°.
Step 4: Divide by 2 to find i.
Answer: 45°

2. A man standing in front of a plane mirror finds his image at a distance 6 metre from himself. What is the distance of man from the mirror ?
Step 1: The total distance from the man to his image is 6 meters.
Step 2: In a plane mirror, object distance to mirror = mirror to image distance.
Step 3: Therefore, the mirror is exactly halfway between the man and his image.
Step 4: Distance = 6 / 2.
Answer: 3 m

3. An insect is sitting in front of a plane mirror at a distance 1 m from it.
(a) Where is the image of the insect formed ?
(b) What is the distance between the insect and its image ?
Step 1: The image forms at the same distance behind the mirror as the object is in front.
Step 2: Since it is 1m in front, the image is 1m behind.
Step 3: The total distance is object distance + image distance (1m + 1m).
Answer: (a) 1 m behind the mirror. (b) 2 m.

4. An object is kept at 60 cm in front of a plane mirror. If the mirror is now moved 25 cm away from the object, how does the image shift from its previous position ?
Step 1: Initially, object is at 60 cm. Image is 60 cm behind mirror. Total distance object to image = 120 cm.
Step 2: Mirror moves 25 cm away. New object distance = 60 + 25 = 85 cm.
Step 3: New image is 85 cm behind new mirror. Total distance object to new image = 170 cm.
Step 4: The object didn't move, so the image shifted by 170 cm - 120 cm = 50 cm.
Answer: 50 cm away from its previous position.

5. An optician while testing the eyes of a patient keeps a chart of letters 3 m behind the patient and asks him to see the letters on the image of chart formed in a plane mirror kept at distance 2 m in front of him. At what distance is the chart seen by the patient ?
Step 1: Calculate the distance of the chart to the mirror. Patient is 2m from mirror, chart is 3m behind patient. So chart is 2m + 3m = 5m from mirror.
Step 2: The mirror forms the chart's image 5m behind the mirror.
Step 3: The patient is looking at the image from their seat, which is 2m in front of the mirror.
Step 4: Total distance from patient to image = 2m (to mirror) + 5m (mirror to image).
Answer: 7 m

EXERCISE-7(B)

(A) MULTIPLE CHOICE TYPE :
(Choose the correct answer from the options given below).

1. In a barber's shop, two plane mirrors are placed :
(a) perpendicular to each other
(b) parallel to each other
(c) at an angle of 60° between them
(d) at an angle of 45° between them.
Step 1: A barber wants you to see the back of your head clearly.
Step 2: This is achieved by placing mirrors directly facing each other on opposite walls.
Answer: (b) parallel to each other

2. For two mirrors kept parallel to each other, the number of images formed is :
(a) 5 (b) 7 (c) 0 (d) infinity
Step 1: Parallel mirrors bounce the light back and forth endlessly.
Step 2: Each bounce creates a new, slightly fainter virtual image.
Answer: (d) infinity

3. The number of images formed for two mirrors kept perpendicular to each other is :
(a) 1 (b) 2 (c) 3 (d) 5
Step 1: Perpendicular mirrors have an angle of 90 degrees.
Step 2: Use the formula n = (360/angle) - 1.
Step 3: n = (360/90) - 1 = 4 - 1 = 3.
Answer: (c) 3

4. A thick plane mirror, silvered at its back, forms multiple number of images. Out of these, the brightest image is :
(a) first image (b) second image
(c) third image (d) All are of equal brightness
Step 1: A thick glass mirror reflects a small amount of light from its front glass surface (1st faint image).
Step 2: The majority of the light enters the glass, hits the strong silver coating at the back, and reflects out.
Step 3: This reflection from the strong silvered back creates the second, brightest image.
Answer: (b) second image

5. How many plane mirrors are used in a periscope and a kaleidoscope ?
(a) 2 and 3 respectively (b) 3 each
(c) 3 and 2 respectively (d) 2 and 4 respectively
Step 1: A periscope uses two mirrors (one to look up, one to bounce light to the eye).
Step 2: A kaleidoscope uses three mirrors arranged in a triangle to create complex patterns.
Answer: (a) 2 and 3 respectively

6. In a kaleidoscope, three plane mirrors are inclined with each other at an angle of :
(a) 0° (b) 30° (c) 60° (d) 90°
Step 1: The three mirrors in a kaleidoscope form an equilateral triangle.
Step 2: The internal angles of an equilateral triangle are all equal to 60 degrees.
Answer: (c) 60°

7. In a periscope, two plane mirrors are inclined at an angle of ......... with the vertical walls.
(a) 0° (b) 30° (c) 45° (d) 60°
Step 1: A periscope needs to bend light exactly 90 degrees to go down the tube.
Step 2: By the law of reflection, to bend light 90 degrees, the mirror must be at half that angle, which is 45 degrees.
Answer: In a periscope, two plane mirrors are inclined at an angle of 45° with the vertical walls. Correct option: (c) 45°

8. Two mirrors are placed at right angles to each other as shown in the figure given below. A ray of light PQ strikes mirror OM at an angle of incidence 30°. What would be its angle of reflection from mirror ON ?
(a) 30° (b) 60° (c) 45° (d) 90°
Step 1: Ray hits first mirror at 30° incidence, so it reflects at 30°.
Step 2: The mirrors are at 90°. Geometrically, the reflected ray creates a right-angled triangle with the mirrors.
Step 3: The angle the ray makes with the second mirror surface is 30°. So the normal to the second mirror makes an angle of 90° - 30° = 60°.
Step 4: Thus, angle of incidence on second mirror is 60°, meaning angle of reflection is also 60°.
Answer: (b) 60°

(B) VERY SHORT ANSWER TYPE :

1. What is the most common use of a plane mirror ?
Step 1: Think of what you use in the bathroom every morning.
Step 2: We use it to see our own reflection.
Answer: Looking glass.

2. How does an optician increase the effective length of his room by using a mirror ? Where does he place the sign board ?
Step 1: An optician needs a 6m distance for eye tests but rooms are often smaller (e.g., 3m).
Step 2: By placing a mirror on the front wall and the sign board on the back wall, the light travels from the board to the mirror and back to the patient.
Step 3: This effectively doubles the room's visual length.
Answer: By keeping a plane mirror on the front wall and placing the sign board on the opposite wall, just behind the patient. The effective length is doubled.

3. What relationship do the images formed by two inclined plane mirrors have for their location with respect to the object placed between them ?
Step 1: When an object is placed between two angled mirrors, it forms multiple images.
Step 2: Geometrically, if you draw a circle using the mirror intersection as the center and the object distance as the radius, all images will perfectly land on this circle's edge.
Answer: All images lie on the circumference of a circle whose centre is at the point of intersection of the two mirrors, with a radius equal to the distance of the object from the intersection.

(C) SHORT ANSWER TYPE :

1. Two plane mirrors are placed making an angle θ in between them. Write an expression for the number of images formed if an object is placed in between the mirrors. State the condition, if any.
Step 1: The primary number to calculate is 360°/θ.
Step 2: If this number is even, one image always overlaps, so we subtract 1.
Step 3: If it is odd, we only subtract 1 if the object is placed perfectly symmetrically in the middle.
Answer: n = (360°/θ) - 1 if 360°/θ is an even integer. If 360°/θ is an odd integer, n = (360°/θ) - 1 when the object is placed symmetrically, and n = 360°/θ when the object is placed asymmetrically.

2. Two plane mirrors are placed making an angle θ° in between them. For an object placed in between the mirrors, if angle is gradually increased from 0° to 180°, how will the number of images change: increase, decrease or remain unchanged ?
Step 1: The formula for number of images relies on dividing 360 by the angle.
Step 2: As the angle (θ) gets larger (increases), dividing 360 by a larger number gives a smaller result.
Answer: Decrease.

3. State two uses of a plane mirror.
Step 1: Think of everyday household uses.
Step 2: Think of scientific or optical instruments.
Answer: (1) As a looking glass for daily use. (2) Inside optical instruments like periscopes and kaleidoscopes.

(D) LONG ANSWER TYPE :

1. How many images are formed for a point object kept in between the two plane mirrors at right angles to each other ? Show them by drawing a ray diagram.
Step 1: Right angles mean 90 degrees. 360/90 = 4 (even). So images = 4 - 1 = 3.
Step 2: Draw an L-shape for the two mirrors. Place object O between them.
Step 3: Draw image I1 behind mirror 1, and image I2 behind mirror 2. Draw I3 at the opposite diagonal corner.
Answer: 3 images are formed. (Diagram: Draw two mirrors meeting at 90°. Place object P. Draw an arc or circle connecting the 3 virtual images that appear behind the mirrors at equal perpendicular distances).

2. Two plane mirrors are arranged parallel and facing each other at some separation. How many images are formed for a point object kept in between them ? Show the formation of images with the help of a ray diagram.
Step 1: Parallel mirrors have an angle of 0. 360/0 is infinity.
Step 2: Light bounces infinitely back and forth between the two mirrors.
Step 3: Draw two vertical lines facing each other, and show zigzag rays bouncing between them endlessly.
Answer: Infinite number of images. (Diagram: Draw two parallel vertical mirrors. Place object P between them. Trace rays going from P, hitting the right mirror to form I1, reflecting back to hit the left mirror to form I2, and so on, continuing backwards infinitely).

(E) NUMERICALS :

1. State the number of images of an object placed between the two plane mirrors, formed in each case when the mirrors are inclined to each other at (a) 90°, and (b) 60°.
Step 1: For 90°, 360/90 = 4 (even). Subtract 1 = 3.
Step 2: For 60°, 360/60 = 6 (even). Subtract 1 = 5.
Answer: (a) 3 images (b) 5 images.

2. An object is placed (i) asymmetrically (ii) symmetrically, between two plane mirrors inclined at an angle of 50°. Find the number of images formed.
Step 1: Calculate 360/50 = 7.2. Since it is a fraction, we take the integral part.
Step 2: If placed asymmetrically, the book's rule states we take the integer 7.
Step 3: If placed symmetrically, an overlap occurs causing us to see 6 images.
Answer: (i) 7 images (ii) 6 images.

EXERCISE-7(C)

(A) MULTIPLE CHOICE TYPE :
(Choose the correct answer from the options given below).

1. A ........... mirror is made by silvering the ........... surface of a piece of a hollow sphere.
(a) convex, outer (b) plane, outer
(c) concave, outer (d) concave, inner
Step 1: A concave mirror curves inwards like a cave.
Step 2: To make the inside reflective, the outside (outer bulging surface) must be painted with silver.
Answer: A concave mirror is made by silvering the outer surface of a piece of a hollow sphere. Correct option: (c) concave, outer

2. A ........... mirror is made by silvering the ......... surface of a piece of a hollow sphere.
(a) concave, inner (b) convex, inner
(c) convex, outer (d) None of the above
Step 1: A convex mirror bulges outwards towards the object.
Step 2: To make the outside reflective, the inside (inner hollow surface) must be painted with silver.
Answer: A convex mirror is made by silvering the inner surface of a piece of a hollow sphere. Correct option: (b) convex, inner

3. The correct statement(s) is/are :
(1) The radius of a sphere of which the spherical mirror is a part is called the radius of curvature.
(2) The geometric centre of the spherical surface of a mirror is called the centre of curvature.
(3) Principal axis is the straight line joining the pole of the mirror to its aperture.
(a) (1) (b) (2)
(c) (3) (d) None of the above
Step 1: Evaluate statement 1: True, radius of curvature is the radius of the original sphere.
Step 2: Evaluate statement 2: False, geometric centre of the mirror surface is the pole, not centre of curvature.
Step 3: Evaluate statement 3: False, principal axis joins pole to centre of curvature, not aperture.
Answer: (a) (1)

4. The focus of a concave mirror is a point on the ......... through which the light rays incident ............ to the principal axis pass after reflection from the mirror.
(a) centre of curvature, perpendicular
(b) principal axis, parallel
(c) principal axis, perpendicular
(d) aperture, parallel
Step 1: The focus is a specific point located on the main centre line (principal axis).
Step 2: It is defined as the spot where incoming rays that are parallel to the principal axis converge.
Answer: The focus of a concave mirror is a point on the principal axis through which the light rays incident parallel to the principal axis pass after reflection from the mirror. Correct option: (b) principal axis, parallel

5. For an incident ray directed towards centre of curvature of a spherical mirror, the reflected ray :
(a) retraces its path (b) passes through the focus
(c) passes through the pole (d) becomes parallel to the principal axis.
Step 1: Any line drawn from the centre of a sphere to its surface is a radius, which acts as the normal (90 degrees).
Step 2: Since the ray travels along the normal, incidence angle is zero, so it bounces straight back.
Answer: (a) retraces its path

6. A ray either incident from the focus (or converging at the focus), after reflection from a spherical mirror :
(a) becomes perpendicular to the principal axis (b) becomes parallel to the principal axis
(c) becomes normal to the focus (d) passes through the centre of curvature
Step 1: This is the exact opposite (reverse principle) of a parallel ray.
Step 2: Just as parallel rays reflect through the focus, rays passing through the focus will reflect out parallel.
Answer: (b) becomes parallel to the principal axis

7. For a concave mirror, when the object is at infinity, the nature of the image formed at focus is :
(a) virtual, inverted (b) virtual, diminished to a point
(c) real, enlarged, inverted (d) real, inverted, diminished to a point
Step 1: Light from infinity arrives as parallel rays.
Step 2: A concave mirror converges parallel rays physically at the focus, making it a real image.
Step 3: Because all rays meet at one single dot, it is point-sized.
Answer: (d) real, inverted, diminished to a point

8. For a concave mirror, when the object is at the centre of curvature, the place and nature of the image formed is :
(a) at focus, real, inverted (b) at focus, virtual, inverted
(c) at centre of curvature, real, inverted, diminished (d) at centre of curvature, real, same size as that of the object
Step 1: Placing an object exactly at C (centre of curvature) is the pivot point for concave mirrors.
Step 2: At this exact spot, the image forms right underneath the object.
Step 3: It is upside down (inverted), real, and exactly the same size.
Answer: (d) at centre of curvature, real, same size as that of the object

9. For a concave mirror, when the object is at focus, the size of the image formed is :
(a) magnified (b) highly magnified
(c) diminished (d) of the same size
Step 1: Putting the object at the focus means the reflected rays shoot out completely parallel.
Step 2: Parallel rays only "meet" at infinity, making the image infinitely large.
Answer: (b) highly magnified

10. The image formed by a convex mirror is :
(a) erect and diminished (b) erect and enlarged
(c) inverted and diminished (d) inverted and enlarged.
Step 1: A convex mirror always diverges light, meaning real intersections never happen.
Step 2: Because of this geometry, the virtual image is always upright (erect) and shrunken down (diminished).
Answer: (a) erect and diminished

11. For a convex mirror, when the object is in front of the mirror, the image formed is :
(a) real, upright and magnified (b) real, inverted and diminished
(c) virtual, upright and magnified (d) virtual, upright and diminished
Step 1: Convex mirrors cannot form real images.
Step 2: The virtual images they form are always smaller than the actual object to fit more in the field of view.
Answer: (d) virtual, upright and diminished

12. The wrong rule of sign convention is :
(1) All distances are measured from the centre of curvature of the mirror taken as origin.
(2) The distances measured along the principal axis in the direction of incident light are positive.
(3) The distances above the principal axis are taken positive.
(a) (1) (b) (2)
(c) (3) (d) both (1) and (2)
Step 1: Review Cartesian sign conventions.
Step 2: The origin point (0,0) is always taken as the pole of the mirror, not the centre of curvature.
Answer: (a) (1)

13. For a convex mirror, the value of u is always ............ and the value of v is .................
(a) positive, positive (b) positive, negative
(c) negative, negative (d) negative, positive
Step 1: Object distance (u) is always measured against the direction of light, making it negative.
Step 2: Convex mirrors always form virtual images behind the mirror, moving in the direction of light, making image distance (v) positive.
Answer: For a convex mirror, the value of u is always negative and the value of v is positive. Correct option: (d) negative, positive

14. A real and enlarged image can be obtained by using a:
(a) convex mirror (b) plane mirror
(c) concave mirror (d) either convex or plane mirror.
Step 1: Plane mirrors make same-size virtual images. Convex mirrors make diminished virtual images.
Step 2: Only concave mirrors can converge light to form real images, which can be enlarged if placed between C and F.
Answer: (c) concave mirror

15. The type of mirror used as a reflector in the street lights is :
(a) plane mirror (b) convex mirror
(c) concave mirror (d) parabolic mirror
Step 1: Street lights need to spread their light over a very large area on the road.
Step 2: Convex mirrors are diverging mirrors, meaning they scatter light outward nicely over a wide area.
Answer: (b) convex mirror

16. The type of mirror used as a shaving mirror in daily life is :
(a) plane mirror (b) convex mirror
(c) concave mirror (d) parabolic mirror
Step 1: When shaving, you need a zoomed-in (magnified) and upright view of your face.
Step 2: A concave mirror provides exactly this type of virtual, enlarged image when your face is close to it (between pole and focus).
Answer: (c) concave mirror

17. Which mirror always forms a diminished image for all positions of the object placed in front of it ?
(a) plane mirror (b) convex mirror
(c) concave mirror (d) parabolic mirror
Step 1: Plane is same size. Concave can be enlarged or diminished.
Step 2: Convex always squeezes the view into a smaller, diminished virtual image.
Answer: (b) convex mirror

18. The figure shows the image of a clock as seen in the plane mirror. The correct time is :
(a) 4:30 (b) 6:30
(c) 2:30 (d) 3:30
Step 1: The image shows 9:30 due to lateral inversion (left-right flip).
Step 2: To find actual time, subtract the mirror time from 12:00. (12:00 - 9:30 = 2:30).
Answer: (c) 2:30

19. We use a concave polished metallic surface as a reflector in a torch to obtain a parallel beam of light. The position of the bulb is :
(a) at the centre of curvature of the reflector.
(b) at the focus of the reflector
(c) between the focus and centre of curvature of the reflector
(d) can be any of the above options
Step 1: To shoot a powerful, straight parallel beam out of a torch, rays need to reflect perfectly parallel.
Step 2: The rule states that rays originating from the focus reflect parallel to the principal axis.
Answer: (b) at the focus of the reflector

(B) VERY SHORT ANSWER TYPE :

1. What is a spherical mirror ?
Step 1: Instead of being flat, imagine a mirror cut out from a hollow glass ball.
Step 2: Formulate this into a definition.
Answer: A reflecting surface which is a part of a sphere is called a spherical mirror.

2. Define centre of curvature of a spherical mirror.
Step 1: Every sphere has a geometric center.
Step 2: The mirror is a piece of that sphere, so it shares the same center.
Answer: The centre of the sphere of which the mirror is a part is called the centre of curvature.

3. Define radius of curvature of a spherical mirror.
Step 1: Similar to the center, every sphere has a radius.
Step 2: The mirror shares the exact same radius as its parent sphere.
Answer: The radius of the sphere of which the spherical mirror is a part is called the radius of curvature.

4. What is the aperture of a spherical mirror ?
Step 1: The aperture is essentially the "window" or the physical size of the mirror piece.
Step 2: It determines how much light can actually enter and strike the surface.
Answer: The plane surface area of the mirror through which light rays enter and fall on the mirror is called its aperture.

5. Define the pole of a spherical mirror.
Step 1: Find the exact physical middle point on the surface of the mirror piece itself.
Step 2: This central dot on the mirror surface is the pole.
Answer: The geometric centre of the spherical surface of the mirror is called the pole of the mirror.

6. Name the spherical mirror which always produces an erect and virtual image. How is the size of image related to the size of object ?
Step 1: Only a convex mirror acts this way consistently for all object positions.
Step 2: It packs a wider view into the mirror, so the objects look smaller.
Answer: Convex mirror. The image is always shorter (diminished) than the size of the object.

7. (a) For what position of object, the image formed by a concave mirror is magnified and erect ?
(b) State whether the image in part (a) is real or virtual?
Step 1: To use a concave mirror as a magnifying glass (erect and large), you must get very close to it.
Step 2: You must be inside its focal length. Being upright means the image is behind the mirror, hence virtual.
Answer: (a) Between the pole and focus. (b) Virtual.

8. (a) State the position of object for which the image formed by a concave mirror is of same size.
(b) Write two more characteristics of the image.
Step 1: The balancing point for a concave mirror is its centre of curvature (C).
Step 2: At C, the image is formed right there, upside down, and can be caught on a screen.
Answer: (a) At the centre of curvature. (b) Real and inverted.

9. (a) What is a real image ?
(b) What type of mirror can be used to obtain a real image of an object ?
(c) Does the mirror mentioned in part (b) form real image for all locations of the object ?
Step 1: Real images involve actual light convergence that can hit a surface.
Step 2: Concave mirrors converge light. Convex mirrors do not.
Step 3: However, if you stand too close (inside focus) to a concave mirror, it behaves virtually.
Answer: (a) A real image is one which is formed by actual intersection of rays and can be obtained on a screen. (b) Concave mirror. (c) No, not when the object is between pole and focus.

10. Name the kind of mirror used to obtain :
(a) a real and enlarged image,
(b) a virtual and enlarged image,
(c) a virtual and diminished image,
(d) a real and diminished image.
Step 1: Only concave can be real. Only concave can enlarge. Convex only makes virtual, diminished.
Step 2: Match the combinations to the mirror capabilities.
Answer: (a) concave, (b) concave, (c) convex, (d) concave.

11. How is the focal length of a spherical mirror related to its radius of curvature ?
Step 1: Geometrically, the focus sits exactly halfway between the pole and the centre of curvature.
Step 2: Therefore, focal length is half the radius.
Answer: f = 1/2 R (Focal length is exactly half of the radius of curvature).

12. Write the spherical mirror's formula and explain the meaning of each symbol used in it.
Step 1: The mirror formula links object distance (u), image distance (v), and focal length (f).
Step 2: They are linked by adding their reciprocals.
Answer: 1/u + 1/v = 1/f. Here, u is object distance from pole, v is image distance from pole, and f is focal length.

13. State the kind of mirror used
(a) by a dentist, (b) as a search-light reflector.
Step 1: Dentists need a magnified view (concave).
Step 2: Search-lights need a powerful parallel beam (concave).
Answer: (a) concave, (b) concave.

14. Which mirror will you prefer to use as a rear view mirror in a car : plane mirror or convex mirror ? Give one reason.
Step 1: A plane mirror gives a 1:1 view, which limits how much of the road you see.
Step 2: A convex mirror shrinks cars down, allowing you to see a much wider area of traffic behind you.
Answer: Convex mirror, because it always provides a virtual, erect image and a much wider field of view.

15. How is magnification (m) related to the distance of the object (u) and the distance of the image (v) ?
Step 1: Magnification describes how many times larger the image is compared to the object.
Step 2: It is calculated by dividing image distance by object distance, with a negative sign for sign convention.
Answer: m = -v/u.

(C) SHORT ANSWER TYPE :
*(Skipping some repetitive definition questions as parsed from the text, focusing on the ones not covered in V.Short)*

6. What is meant by magnification ? Write its expression. What is its sign for the (a) real (b) virtual, image ?
Step 1: Magnification is the ratio of image height to object height.
Step 2: Real images are inverted (negative height), making m negative.
Step 3: Virtual images are upright (positive height), making m positive.
Answer: Magnification is the ratio of length of the image to the length of the object (m = I/O or -v/u). (a) For a real image, sign is negative. (b) For a virtual image, sign is positive.

(D) LONG ANSWER TYPE :
*(Diagram drawing steps)*

1. Draw suitable diagrams to illustrate the action of (i) concave mirror, (ii) convex mirror, on a beam of light incident parallel to the principal axis.
Step 1: For concave, draw parallel rays hitting the inner curve and bouncing inward to cross exactly at F.
Step 2: For convex, draw parallel rays hitting the outer curve and bouncing outward, with dotted lines extending back to F.
Answer: (i) In concave mirror, parallel rays converge at a real focus in front of the mirror. (ii) In convex mirror, parallel rays diverge and appear to come from a virtual focus behind the mirror. (Draw corresponding ray diagrams).

(E) NUMERICALS :

1. The radius of curvature of a convex mirror is 40 cm. Find its focal length.
Step 1: The formula connecting focal length (f) and radius of curvature (R) is f = R/2.
Step 2: Substitute R = 40 cm into the equation.
Step 3: f = 40 / 2 = 20 cm.
Answer: 20 cm

2. The focal length of a concave mirror is 10 cm. Find its radius of curvature.
Step 1: If f = R/2, then rearranging gives R = 2 * f.
Step 2: Substitute f = 10 cm into the equation.
Step 3: R = 2 * 10 = 20 cm.
Answer: 20 cm

11. A concave mirror forms a virtual image of size twice that of the object placed at a distance 5 cm from it. Find: (a) the focal length of the mirror (b) position of image.
Step 1: Magnification m = +2 (positive because virtual images are erect). Object distance u = -5 cm.
Step 2: Use m = -v/u. So, 2 = -v/(-5). Solving this gives v = 10 cm (image position).
Step 3: Use mirror formula: 1/f = 1/v + 1/u.
Step 4: 1/f = 1/10 + 1/(-5) = 1/10 - 2/10 = -1/10. So f = -10 cm.
Answer: (a) 10 cm (magnitude). (b) 10 cm behind the mirror.

(F) ASSERTION – REASON TYPE QUESTIONS :
(Choose the answer based on the codes given below.)
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are True and R is not the correct explanation of A
(c) Assertion is false but reason is true
(d) Assertion is true but reason is false

(i) Assertion (A) : For a ray of light incident at an angle of incidence i = 0°, angle of reflection is r = 0°.
Reason (R) : The angle of incidence i is equal to angle of reflection r.
Step 1: The assertion claims a 0 degree hit yields a 0 degree reflection, which is true.
Step 2: The reason states the law of reflection (i = r), which perfectly explains the assertion.
Answer: (a) Both A and R are true and R is the correct explanation of A

(ii) Assertion (A) : The image of an object placed close to a concave mirror is a real image.
Reason (R) : A real image is formed due to the actual intersection of the reflected rays.
Step 1: If an object is placed very close (inside focus) to a concave mirror, it acts as a magnifying glass and forms a virtual image, making the Assertion false.
Step 2: The Reason's definition of a real image is scientifically true.
Answer: (c) Assertion is false but reason is true

(iii) Assertion (A) : For a real image formed by a spherical mirror, linear magnification (m) is positive.
Reason (R) : Both u and v are negative for a real image.
Step 1: Real images are inverted, meaning magnification (m) must be negative. Assertion is false.
Step 2: For real images in mirrors, the object and image are on the same side, making both u and v negative. Reason is true.
Answer: (c) Assertion is false but reason is true

(iv) Assertion (A) : For an object placed symmetrically when the angle θ between the mirrors is 72°, the number of images formed is 4.
Reason (R) : If n = 360°/θ is odd, the number of images for an object placed symmetrically is equal to n.
Step 1: 360/72 = 5 (odd). If symmetric, we subtract 1, so images = 4. Assertion is true.
Step 2: Reason claims number of images is n (which would be 5). But it is actually n - 1. Reason is false.
Answer: (d) Assertion is true but reason is false

(v) Assertion (A) : Concave mirror is used as doctor's head mirror.
Reason (R) : If a parallel beam of light is incident on a concave mirror, the mirror focuses the beam to a point.
Step 1: Doctors use head mirrors to concentrate light, which is concave. True.
Step 2: The reason correctly states concave mirrors focus parallel light to a specific point, aiding the doctor. True and correct explanation.
Answer: (a) Both A and R are true and R is the correct explanation of A

(vi) Assertion (A) : A student is given a spherical mirror of focal length - 10 cm. He identifies it as a concave mirror.
Reason (R) : Focal length of a concave mirror is always positive.
Step 1: By sign convention, concave mirrors have a focus on the left (negative side). So Assertion is true.
Step 2: Reason claims concave focal length is positive, which is completely false.
Answer: (d) Assertion is true but reason is false

(G) CASE STUDY BASED QUESTIONS :

1. A student stands between two parallel plane mirrors facing each other. Later, one of the plane mirrors is replaced with a convex mirror.
(a) Why are multiple images formed between two plane mirrors?
(b) When one plane mirror is replaced by a convex mirror, predict how the number and nature of images will change.
(c) If the two plane mirrors are kept perpendicular to each other, what will be the number of images formed?
(d) How many mirrors are used in a kaleidoscope and at what angle are they inclined?
Step 1: Parallel mirrors bounce light infinitely.
Step 2: A convex mirror bulges, spreading rays out, so fewer rays bounce back to the other mirror, reducing images.
Step 3: 360/90 - 1 = 3 images for perpendicular.
Step 4: Kaleidoscopes use triangle geometry (3 mirrors, 60 degrees).
Answer:
(a) Due to multiple reflections of light back and forth between the two mirrors.
(b) Number of images will decrease and the image becomes diminished and less distinct.
(c) 3
(d) Three mirrors inclined at 60°.

2. A car engineer tested different types of mirrors for side-view purposes.
One mirror produced accurately-sized images but with a limited field of view. Another mirror produced smaller images but provided a wider field of view.
(a) Which type of mirror should be preferred for side-view purposes? Give reason.
(b) State the quality of the image formed by the mirror answered by you above in (a).
(c) Can the same mirror be used as a doctor's head mirror? Give reason.
(d) State two other uses of the mirror used above in (a).
Step 1: Driving requires seeing as much of the road behind you as possible, requiring a wide field of view.
Step 2: The mirror offering a wide view creates small, upright, virtual images (convex).
Step 3: Doctors need focusing (concave), not diverging (convex).
Step 4: Convex mirrors are good anywhere wide security viewing is needed.
Answer:
(a) The mirror producing smaller images with a wider field of view (convex mirror) should be preferred, as it helps the driver see a larger area of traffic behind.
(b) Virtual, erect, and diminished.
(c) No, a doctor needs a concave mirror to focus incoming light onto a small point.
(d) As a reflector in street lamps and as security mirrors in shops.