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

Step-by-step 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 = (Sin i)/(Sin r)`

By substituting the values, we get

`t = (Sin i)/(Sin (i)/(2))`

By using the formula of trigonometry

Sin2Ф = 2 SinФ CosФ

So,
`t = (2Sin (i)/(2)* Cos(i)/(2))/(Sin (i)/(2))`

`t = 2Cos(i)/(2)`

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

`1.5 = 2Cos(i)/(2)`

`Cos(i)/(2)=0.75`

`(i)/(2)=41.4`

i = 82.8°