Question

a given monochromatic light rat initially in air strikes the first face of prism
of refracting angle 90 if the ray emerges grazing the second face the angle of incidence on the first face is

Answer 1

Answer:

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Answer 2

The angle of incidence on the first face will be $sin^{-1} [90n-nsin^{-1} (\frac{1}{n} )]$

Given:

A monochromatic light ray initially in the air strikes the first face of the prism.

The refracting angle of the prism (A) = 90°

The ray emerges grazing on the second face which means the angle of emergence is 90°.

To Find:

The ray of incidence on the first face of the prism.

Solution:

Let us assume that the angle of incidence is i.

r1 is the angle of refraction on the first face and r2 is the angle of incidence on the second face.

n is the refractive index of the material of the prism.

According to snell's law:

$n=\frac{sin i}{sinr1}$(For the first face)........(i)

and, $n=\frac{sin90}{sinr2}$

⇒$sinr2=\frac{1}{n}$

⇒ $r2= sin^{-1} (\frac{1}{n} )$

We know that, r1+r2=A

Here A=90°

So, r1+r2=90°

r1= 90°-r2

$r1= 90-sin^{-1} (\frac{1}{n} )$

According to eq. (i),

$n=\frac{sin i}{sinr1}$

⇒$sini= 90n-nsin^{-1} (\frac{1}{n})$

⇒$i= sin^{-1} [90n-nsin^{-1} (\frac{1}{n} )]$

Hence, the angle of incidence on the first face of the prism is $sin^{-1} [90n-nsin^{-1} (\frac{1}{n} )]$

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