Question

Velocity of light travelling from rarer medium to denser medium is decreased by 30%. Find the refractive index of denser medium with respect to rarer medium ?
1. 1.35
2. 1.5
3. 1.4
4. 1.428

Answer 1

Correct Answer - Option 4 : 1.428

CONCEPT:

• Absolute refractive index of a medium: The ratio of the speed of light in air or vacuum to the speed of light in the given medium is called the absolute refractive index of the medium.

μ = c / v

μ is the absolute refractive index, c is the speed of light in air, v is the speed of light in the given medium

• Relative refractive index: The ratio of the speed of light in a transparent medium 1 to the speed of light in transparent medium 2 is called the refractive index of medium 2 with respect to medium 1.
• In general, the refractive index is a term used for absolute refractive index. 
• The optical denser medium will have a higher refractive index and lower speed of light in it. 

The speed of light in air is approximately equal to 3 × 10 8 m /s 

If we convert, meter to the centimeter, the speed of light will be

c = 3 × 10 8 × 10 2 cm /s

= 3 × 10 10 cm / s

CALCULATION:

So, the relative refractive index is given as, 

\(\mu = \frac{v_1}{v_2}\)        ---(1)

v₁ is the speed of light in the optically rarer medium, v₂ is the speed of light in the optically denser medium.

v₁ > v₂

v₁ is decreased by 30 %,

v₂ = v₁ - 30 % of v₁ = 0.7 v₁       ---(2)

Putting (2) in (1)

\(\mu = \frac{v_1}{0.7 \ v_1} = 1.428\)

So, the correct option is 1.428.