Question

A light ray in air is incident on a transparent material whose index of refraction is t. o. Find an expression for the (non-zero) angle of incidence whose angle of refraction is half the angle of incidence. b. Evaluate your expression for light incident on glass.

Answer 1

Answer:

Explanation:

Refractive index f the medium, n = t

Let the angle of incidence is i

(a) As given in the question, the angle of refraction is half of angle of incidence.

Let the angle of refraction is r

r = i / 2

By use of Snell's law

$n = \frac{Sin i}{Sin r}$

By substituting the values, we get

$t = \frac{Sin i}{Sin \frac{i}{2}}$

By using the formula of trigonometry

Sin2Ф = 2 SinФ CosФ

So, $t = \frac{2Sin \frac{i}{2}\times Cos\frac{i}{2}}{Sin \frac{i}{2}}$

$t = 2Cos\frac{i}{2}$

(b) For glass, the value of refractive index is 1.5, so the above expression becomes

$1.5 = 2Cos\frac{i}{2}$

$Cos\frac{i}{2}=0.75$

$\frac{i}{2}=41.4$

i = 82.8°