Question

The refractive indices of quartz and salt water are 1.54 and 1.33 respectively, in which of the given mediums light will be faster and by  what factor with respect to other medium 
1. 1.1 V_2, quartz
2. 1.1V₁, Salt water
3. 1.3 V₂, Quartz
4. 1.3 V₁, Salt water

Answer 1

Correct Answer - Option 2 : 1.1V₁, Salt water

CONCEPT: 

• The refractive index, a dimensionless number which is defined as the ratio of the velocity of light in a vacuum to the velocity of light in a medium and is given by

\(⇒ n = \frac{C}{V}\)

Where C = Velocity of light, V= Velocity of light in the medium

• The refractive index is the measure of the degree of bending of light as it passes from one medium to another, or it is the measure of the optical density of the medium
• More the refractive index of the medium, the lesser will be the speed of light in the medium.

EXPLANATION:

Given -  n₁ = 1.54, n₂ = 1.33 and let V₁ = Velocity of light in quartz, V₂ = Velocity of light in salt water

• The refractive index is given by

\(⇒ n = \frac{C}{V}\)

From the above equation, it is clear that the more the refractive index of the medium the lesser will be the speed of light in the medium.

• The refractive index of quartz is greater than saltwater (n₁ > n₂) which means the velocity of light in saltwater is greater than that of quartz (V₂ > V₁)
• The ratio of refractive indices is given by

\(⇒ \frac{n_{1}}{n_{2}} = \frac{V_{2}}{V_{1}}\)

\(⇒ \frac{1.54}{1.33} = \frac{V_{2}}{V_{1}}\)

\(⇒ \frac{V_{2}}{V_{1}} = 1.1\)

⇒ V₂ = 1.1 V₁

• The velocity of light in saltwater will be greater than that of quartz and by a factor of 1.1 V₁
• Hence, option  2  is the answer