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# Numerical problems

8th Science : Chapter 3 : Light : Numerical Example solved problems and book back Numerical problems Questions with Solution

Problem 1

The radius of curvature of a spherical mirror is 20 cm. Find its focal length.

Solution

Radius of curvature = 20 cm

Focal length (f) = Radius of curvature / 2

= R/2 = 20/2 = 10 cm

Problem 2

Focal length of a spherical mirror is 7 cm. What is its radius of curvature?

Solution

Radius of curvature (R) = 2 × Focal length

= 2 × 7 = 14 cm Problem 3

If two plane mirrors are inclined to each other at an angle of 90°, find the number of images formed.

Solution

Angle of inclination = 90°

Number of umber of images formed = [360°/θ] – 1

[360°90°] –1= 4-1=3

Problem 4

Speed of light in air is 3 × 108 m s-1 and the speed of light in a medium is 2 ×108 ms-1. Find the refractive index of the medium with respect to air.

Solution

Refractive index (μ) = Speed of light in air (c) / Speed of light in the medium (v)

μ = 3×108 / 2×108 = 1.5

Problem 5

Refractive index of water is 4/3 and the refractive index of glass is 3/2. Find the refractive index of glass with respect to the refractive index of water.

Solution

wμg = Refractive index of glass / Refractive index of water

= (3/2) / (4/3) = 9/8 = 1.125

1. The radius of curvature of a spherical mirror is 25 cm. Find its focal length.

Given : Radius of curvature = 25 cm

To find : f = ?

Solution : f = R/2 = 25/2

f = 12.5 cm

2. If two plane mirrors are inclined to each other at an angle of 45°, find the number of images formed.

Given :  Angle of inclination = 45o

To find : Number of images formed = [ 360/ angle ] − 1

Solution :

[ 36045−1

= 8 – 1 = 7 images

3. Speed of light in air is 3 × 108 m s–1 and the refractive index of a medium is 1. 5. Find the speed of light in the medium.

Given : Speed of light in air c = 3 × 108 ms-1

Refractive index of a medium μ = 1.5

To find : Speed of light in medium v = ?

Formula : μ= c/v

Solution : 1.5 = [ 3 × 10] / v

V = [3×108] / 1.5

v = 2 × 108 ms-1

Speed of light in medium v = 2 × 108 ms-1

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