Answer to Question #200379 in Optics for Piolo

Question

A light beam in air is incident on the surface of a pond, making an angle of 21° with respect to the surface. What are the angles of refraction?

answer to 2 decimal places

Answer 1

Refractive Index: It is defined as the ratio of the velocity of light in a vacuum to the velocity of light in a particular medium.

$n= \frac{c}{v}$

where,

n = refractive index of the material

c = speed of light in vacuum

v = speed of light in the material

According to the first law of reflection of light, the angle of incidence is always equal to the angle of reflection.

We have the first medium through which the light beam is incident is air, which have a refractive index of 1.000293

The second medium is air which have a refractive index of 1.33

Incident angle 90^o−21^o=69°

From the formula, angle of refraction

$n_2sinθ_r=n_1sinθ_i \\ θ_r=sin^{-1}(\frac{n_1sinθ_i}{n_2}) \\ = sin^{-1}(\frac{1.000293sin(69^o)}{1.33}) \\ = 44.60^o$

The angle of refraction is 44.60°