Question

A ray of light incident on one face of equilateral glass prism is refracted in such a way that it emerges from opposite surface at an angle of 90 to the normal. Calculate the angle of incidence​

Answer 1

i ≅
`28^(0)`

Step-by-step explanation:

Let the angle of incidence be represented by i, angle of emergence be represented by e, and angle of refraction by r.

Snell's law states that;

n =
`(sin i)/(sin r)` ................ 1

where n is the refractive index of the prism.

Given that emergence =
`90^(0)`

But from a ray diagram for the given question, we have;

`60^(0)` + (
`90^(0)` - r) + (
`90^(0)` -
`r^(I)`) =
`180^(0)` (sum of angles in a triangle) .................. 2

(
`90^(0)` - r ) + (
`90^(0)` -
`r^(I)` ) =
`180^(0)` -
`60^(0)`

180° - (r +
`r^(I)`) =
`180^(0)` -
`60^(0)`

r +
`r^(I)` =
`60^(0)`

⇒ r =
`60^(0)` -
`r^(I)` ........................ 3

The refractive index of the equilateral prism = 1.5.

Applying Snell's law to the refracting surface,

`(sinr^(I) )/(sin e)` =
`(1)/(n)`

`(sinr^(I) )/(sin 90^(0) )` =
`(1)/(1.5)`

⇒
`r^(I)` =
`41.81^(0)`

From equation 3,

r =
`60^(0)` -
`r^(I)`

r =
`60^(0)` -
`41.81^(0)`

r =
`18.19^(0)`

So that ;

n =
`(sin i)/(sin r)`

1.5 =
`(sin i)/(sin18.19^(0) )`

sin i = 0.4683

i =
`27.92^(0)` ≅
`28^(0)`