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

Answer:

Liquid's index of refraction, n₁ = 1.27

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, $\theta_2=90$

$sin\theta_c=\dfrac{n_2}{n_1}$

Where

n₂ = Refractive index of air = 1

n₁ = refractive index of liquid

So,

$n_1=\dfrac{n_2}{sin\theta_c}$

$n_1=\dfrac{1}{sin(52)}$

n₁ = 1.269

or n₁ = 1.27

Hence, the refractive index of liquid is 1.27