Refractive Index Numericals class 10 & practice problems

Last updated on October 29th, 2023 at 03:19 pm

Refractive Index Numericals class 10 – In this post, we will solve a bunch of Numerical problems using the refractive index formulas (from the Light chapter in class 10 Physics). The refractive index is written as RI as well. Students may follow the RI practice problems as well (all solved), to understand the inherent concepts of RI. The formulas used to solve these numericals are also given separately on this page.

Refractive Index Formulas to use

Here, is a list of formulas that will help to solve the refractive index numerical problems for class 10.

1. (Absolute Refractive Index – also called Refractive index or RI of a medium)
   µ = speed of light in vacuum (or air) / speed of light in that medium = c/V
2. ₁µ₂ = RI of the second medium with respect to the first medium
   = (speed of light in medium 1) / (speed of light in medium 2)
3. ₁µ₂ = RI of the second medium with respect to the first medium
   = (Absolute RI of the second medium) / (Absolute RI of the first medium)
4. ₂μ₁ = ₁μ₂
   This means, the RI of the first medium with respect to the second medium = 1 / [RI of the second medium with respect to the first medium]
5. Refractive index = Real depth/apparent depth
6. The refractive index of the medium where refraction happens with respect to the medium where the incidence of light happens = sine of the angle of incidence/sine of the angle of refraction
   => µ = sin i/sin r (Snell’s Law)

Refractive Index Numerical problems for class 10

Q1 ] The speed of light in air is 3 x 10^8 m/s and in glass, it is 2×10^8 m/s. The RI of glass is ________________.
Solution:
RI of glass = speed of light in air /speed of light in glass = (3 x 10^8)/(2 x 10^8) = 1.5

Q2 ] The speed of light in water is 2.25 x 10^8 m/s. So the RI of water is:
Solution:
_air µ_water = C / V
= speed of light in air/speed of light in water
= ( 3 x 10^8) / (2.25 x 10^8) =1.33

Q3 ] The RI of the diamond is 2.41. What is the speed of light in a diamond?
Solution:
RI of diamond = speed of light in air /speed of light in the diamond
=> µ_diamond =C / V_diamond
=> V_{diamond =} C / µ_diamond
= (3 x 10^8) / 2.41 m/s = 1.24 x 10^8 m/s

4 ] The refractive index(RI) of glass is 1.5 and that of water is 1.33.
What is the RI of glass with respect to water?
What is the RI of water with respect to glass?

Solution:
The Refractive index(RI) of glass (µ_glass)is 1.5
and Refractive index(RI) of water(µ_water) is 1.33
Now, RI of glass with respect to water
= _waterµ_glass = µ_glass / µ_water = 1.5 /1.33 = 1.127

RI of water with respect to glass = _glassµ_water = µ_water / µ_glass = 1.33/1.5 = 0.89

Practice problems (solved) based on RI formulas

1 ] Light travels from a rarer medium 1 to a denser medium 2. The angle of incident and refraction are respectively 45⁰ and 30⁰. Calculate the refractive index of medium 2 with respect to the medium 1

Solution:
refractive index of the medium 2 with respect to the medium 1 = sin i/sin r = sin 45/sin 30 = 1.41

2 ] A pond of depth 40 cm is filled with water of refractive index 4/3. Calculate the apparent depth of the tank when viewed normally.

Solution:
refractive index = real depth/apparent depth
=> apparent depth = real depth/refractive index = 40/(4/3) = 30 cm

3 ] Calculate the speed of light in water of refractive index 4/3.

Solution:
RI of water = speed of light in air /speed of light in water
=> µ_w =C / V_w
=> V_{w =} C / µ_w
= (3 x 10^8) / (4/3) m/s = 2.25 x 10^8 m/s

4 ] How much time will light take to cross a 5 mm thick glass pane if the refractive index of glass is 3/2?

Solution:

RI of glass = speed of light in air /speed of light in glass
=> speed of light in glass= speed of light in air /RI of glass
=> speed of light in glass = (3 x 10^8)/(3/2) = 2 x 10^8 m/s
Time taken = distance/speed = thickness of glass pane/speed of light in glass
=5 x 10^-3 / 2 x 10^8 sec = 2.5 x 10^-11 sec

5 ] A ray of light passes from air to glass (RI = 1.5) at an angle of 30⁰. Calculate the angle of refraction.

Solution:
Refractive index of glass with respect to air = sin i/sin r
=> 1.5= sin 30/sin r
=>sin r = sin 30/1.5 = 1/3
=>So, angle of refraction r = 19.27⁰

6 ] A ray of light is incident on a glass slab at an angle of 45⁰. If the refractive index of glass is 1.6, what is the angle of refraction?

Solution:
i = 45⁰
The refractive index of glass µ_glass = 1.6
Refraction angle r =?
We know that µ_glass = sin i/sin r
=> sin r = sin i / µ_glass = sin 45⁰ / 1.6 = 0.442
r = 26.23⁰

RI Numerical problems assignment (10 problems to solve)

Summary

To solve numerical problems on the refractive index, we need to use any one of the above-listed formulas, depending on the given data and the required quantity.