Question

Tha ray of light is incident normally in one surface of a prism of reftacting angle 60. The emergent ray grazes the other refracting surface. Find the refractive index of the prism.

Answer 1

$\huge\underline{\underline{\bf \orange{Question-}}}$

Tha ray of light is incident normally in one surface of a prism of reftacting angle 60. The emergent ray grazes the other refracting surface. Find the refractive index of the prism.

$\huge\underline{\underline{\bf \orange{Solution-}}}$

Tha ray of light is incident normally in one surface of a prism (Given)

⛬ ${\sf r_1}$ = 0

and Prism refracting angle (∠A) = 60°

So ,

$\implies{\sf \red{ r_1+r_2=\angle A} }$

$\implies{\sf 0+ r_2=60°}$

$\implies{\sf \green{ r_2=60°} }$

${\sf r_2}$ is critical angle for prism

✪$\large{\boxed{\bf \blue{\mu=\dfrac{1}{sin\theta_c}} }}$

$\implies{\sf \mu=\dfrac{1}{sin\:r_2}}$

$\implies{\sf \mu=\dfrac{1}{sin60°} }$

$\implies{\sf \mu=\dfrac{1}{\sqrt{3}/2}}$

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

On rationalisation

$\implies{\sf \mu=\dfrac{2}{\sqrt{3}}×\dfrac{\sqrt{3}}{\sqrt{3}} }$

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

$\implies{\sf \mu=\dfrac{2×1.732}{3} }$

$\implies{\sf \mu= \dfrac{3.46}{3}}$

$\implies{\bf \red{ \mu=1.15 }}$

$\huge\underline{\underline{\bf \orange{Answer-}}}$

Refractive index of the prism is ${\bf \red{1.15}}$.