Question

A Ray of light is incident normally on a Prism of refractive index 1.5 as shown. The prism is immersed in a liquid of refractive index 'u'. The largest value of angle ACB, so that the ray is totally reflected at the face AC is 30°. then the value of u must be:
1)√3/2
2)5/3
3)4/3
4)3√3/4​

Answer 1

Given that,

Refractive index of prism = 1.5

Reflected angle = 30°

We need to calculate the incidence angle

Using formula of incidence angle

$i+r=90$

Put the value into the formula

$i=90-30$

$i=60^{\circ}$

θ at the glass and liquid interface

We need to calculate the angle

Using snell's law

$\mu_{g}\sin\theta_{c}=\mu\sin90$

$\sin\theta_{c}=\dfrac{\mu}{\mu_{g}}\sin90$

Put the value into the formula

$\sin\theta=\dfrac{\mu}{1.5}$

$\sin\theta=\dfrac{2\mu}{3}$

$\theta_{c}=\sin^{-1}(\dfrac{2\mu}{3})$

We need to calculate the value of μ

Using formula of incidence angle

$\sin i = \sin\theta_{c}$

$\sin60 =\sin\theta_{c}$

Put the value into the formula

$\dfrac{\sqrt{3}}{2}=\dfrac{2\mu}{3}$

$\mu=\dfrac{3\sqrt{3}}{4}$

Hence, The value of μ is $\dfrac{3\sqrt{3}}{4}$

(4) is correct option.