Step 1: Use the plane mirror rule. For a plane mirror, image distance = object distance.

Object distance from mirror = 2.5 m

Step 2: Calculate image distance.

Image distance from mirror = 2.5 m (behind the mirror)

Step 3: Find the distance between object and image.

Distance between boy and his image = distance from boy to mirror + distance from mirror to image = 2.5 m + 2.5 m = 5.0 m

Answer: The image is 2.5 m behind the mirror and 5.0 m away from the boy.

Step 1: Initial distances.

Initial object distance from mirror = 1.8 m Initial image distance from mirror = 1.8 m

Initial separation = 1.8 m + 1.8 m = 3.6 m

Step 2: After the girl moves 0.4 m towards the mirror.

New object distance = 1.8 m − 0.4 m = 1.4 m New image distance = 1.4 m

New separation = 1.4 m + 1.4 m = 2.8 m

Answer: Initial separation = 3.6 m, new separation after moving closer = 2.8 m.

Step 1: Original distance between child and image.

Original object distance = 3.0 m Original image distance = 3.0 m

Original separation = 3.0 m + 3.0 m = 6.0 m

Step 2: New distance after moving 0.7 m away.

New object distance = 3.0 m + 0.7 m = 3.7 m New image distance = 3.7 m

New separation = 3.7 m + 3.7 m = 7.4 m

Step 3: Change in separation.

Change = New separation − Original separation = 7.4 m − 6.0 m = 1.4 m increase

Answer: The distance between the child and image increases by 1.4 m.

Step 1: Let the new distance from the mirror be d metres.

Then, distance between man and image = 2 × d.

We are told this separation should be 2.0 m.

Step 2: Form and solve the equation.

2 × d = 2.0 ⇒ d = 2.0 / 2 = 1.0 m

Step 3: Find how much he moves.

Original distance from mirror = 2.2 m New distance from mirror = 1.0 m

Distance moved towards mirror = 2.2 m − 1.0 m = 1.2 m

Answer: He must move 1.2 m towards the mirror.

Step 1: Use the relation for distance between object and image.

Distance between object and image = 2 × (object distance from mirror)

Let new object distance be d m.

Step 2: Substitute the given data.

2 × d = 5.0 ⇒ d = 5.0 / 2 = 2.5 m

Answer: The new distance of the object from the mirror is 2.5 m.

Concept: To see the full image, the minimum mirror length must be half the height of the person.

Step 1: Height of girl = 1.4 m

Step 2: Minimum mirror length = (1/2) × height of girl = (1/2) × 1.4 m = 0.7 m

Answer: The minimum mirror length needed is 0.7 m.

Step 1: Minimum mirror length required = half the height of boy.

Required mirror length = (1/2) × 1.5 m = 0.75 m

Step 2: Compare with the actual mirror length.

Actual mirror length = 0.9 m, which is greater than 0.75 m.

Answer: Yes, he can see his full image. Minimum required length is 0.75 m, and his mirror is 0.9 m long.

Step 1: Find required minimum mirror length.

Required mirror length = (1/2) × child’s height = (1/2) × 1.2 m = 0.6 m

Step 2: Compare with current mirror.

Current mirror length = 0.5 m

Extra length needed = 0.6 m − 0.5 m = 0.1 m

Answer: The mirror length must be increased by 0.1 m (10 cm).

Step 1: Check requirement for the 1.6 m tall man.

Required mirror length = (1/2) × 1.6 m = 0.8 m (Exactly equal to the mirror length, so he just sees his full image.)

Step 2: Check requirement for the 1.8 m tall person.

Required mirror length = (1/2) × 1.8 m = 0.9 m

Step 3: Compare with actual mirror length (0.8 m).

0.9 m > 0.8 m, so the second person cannot see his full image.

Answer: No, the 1.8 m tall person cannot see his full image in the same 0.8 m mirror.

Step 1: Minimum mirror length = half of student’s height.

= (1/2) × 1.3 m = 0.65 m

Step 2: Convert to centimetres.

1 m = 100 cm 0.65 m = 0.65 × 100 cm = 65 cm

Answer: She should buy a mirror of at least 65 cm length.

Formula: Number of images N = (360° / θ) − 1

Step 1: Substitute θ = 60°.

N = (360° / 60°) − 1 = 6 − 1 = 5

Answer: 5 images of the object will be seen.

Formula: N = (360° / θ) − 1

Step 1: Here θ = 90°.

N = (360° / 90°) − 1 = 4 − 1 = 3

Answer: 3 images of the object will be formed.

Formula: N = (360° / θ) − 1

Step 1: Given N = 8

8 = (360° / θ) − 1

Step 2: Rearrange to find θ.

(360° / θ) = 8 + 1 = 9 ⇒ θ = 360° / 9 = 40°

Answer: The angle between the mirrors is 40°.

Formula: N = (360° / θ) − 1

Step 1: For θ = 45°

N = (360° / 45°) − 1 = 8 − 1 = 7

Answer: 7 images will be formed.

Formula: N = (360° / θ) − 1

Step 1: θ = 30°

N = (360° / 30°) − 1 = 12 − 1 = 11

Answer: 11 images will be seen.

Given: Speed of light, v = 3 × 10⁸ m/s Time, t = 8 minutes

Step 1: Convert time into seconds.

t = 8 minutes = 8 × 60 s = 480 s

Step 2: Use distance formula Distance = speed × time.

Distance, d = v × t = (3 × 10⁸ m/s) × 480 s = 3 × 480 × 10⁸ m = 1440 × 10⁸ m = 1.44 × 10¹¹ m

Answer: The Sun is approximately 1.44 × 10¹¹ metres from the Earth.

Given: Speed of sound, v = 340 m/s Time delay, t = 5 s

Step 1: Use Distance = Speed × Time.

Distance = 340 m/s × 5 s = 1700 m

Answer: The thundercloud is approximately 1700 m (1.7 km) away from the person.

Concept: Light travels in straight lines, so the bright spot on the wall appears where light falls on the wall.

Step 1: Initial distance from torch to wall = 2 m

Step 2: New distance from torch to wall = 5 m

Step 3: Increase in distance = 5 m − 2 m = 3 m

Answer: The distance between the torch and the bright spot on the wall increases by 3 m.

Given: Number of characters = 45 Average raised dots per character = 3

Step 1: Total raised dots = Number of characters × dots per character.

Total dots = 45 × 3 = 135

Answer: The student feels 135 raised dots while reading that Braille line.

Given: Reading rate = 20 pages per hour

Step 1: Time available = 2.5 hours

Step 2: Total pages read = Rate × Time

Total pages = 20 pages/hour × 2.5 hours = 50 pages

Answer: The student can read 50 pages in 2.5 hours.