Question

A ray of light is incident on a plane surface separating two sheets of glass with refractive indexes 1.70 and 1.58. The angel of incidence is 62.0, and the ray originates in the glass with n=1.70. Computer the angle of refraction.

Answer 1

Answer:

Angle of refraction, $\theta_{r} = 71.804^{\circ}$

Solution:

As per the question:

Refractive index of the first sheet, $mu_{a} = 1.70$

Refractive index of the second sheet, $mu_{b} = 1.58$

Angle of incidence, $\theta_{i} = 62.0^{\circ}$

Now, according to Snell's Law:

$\mu_{a}sin\theta_{i} = \mu_{b}sin\theta_{r}$          (1)

$\theta_{r}$ = Angle of refraction

From eqn(1), angle of refraction may be computed as:

$sin\theta_{r} = \frac{\mu_{a}}{\mu_{b}}sin\theta_{\theta_{i}}$

$sin\theta_{r} = \frac{1.70}{1.58}sin(62^{\circ})$

$\theta_{r} = sin^{- 1}(0.9499) = 71.804^{\circ}$

Answer 2

Answer:

r = 71.8⁰

Explanation:

given,

refractive index of the glass 1 = 1.70

refractive index of glass 2 = 1.58

angle of incidence = 62°

angle of refraction =?

using Snell's law

$\dfrac{sin\ i}{sin\ r} = \dfrac{n_2}{n_1}$

$\dfrac{sin\ 62^0}{sin\ r} = \dfrac{1.58}{1.70}$

1.7 ×sin 62 ^0 = 1.58× sin r

$sinr = \dfrac{1.7\times sin 62^0}{1.58}$

sin r = 0.95

r = sin⁻¹(0.95)

r = 71.8⁰

angle of refraction =r = 71.8⁰