Question

The critical angle for a liquid in air is 520, What is the liquid's index of refraction? 0.62 0.79 1.27 1.50

Answer 1

Liquid's index of refraction, n₁ = 1.27

Step-by-step explanation:

It is given that,

The critical angle for a liquid in air is,
`\theta_c=52^o`

We have to find the refractive index of the liquid. Critical angle of a liquid is defined as the angle of incidence in denser medium for which the angle of refraction is 90°.

Using Snell's law as :

`n_1sin\theta_c=n_2sin\theta_2`

Here,
`\theta_2=90`

`sin\theta_c=(n_2)/(n_1)`

Where

n₂ = Refractive index of air = 1

n₁ = refractive index of liquid

So,

`n_1=(n_2)/(sin\theta_c)`

`n_1=(1)/(sin(52))`

n₁ = 1.269

or n₁ = 1.27

Hence, the refractive index of liquid is 1.27