Question

The absolute indices of refraction of diamond and crown glass are 5/2 and 3/2 respectively.
The critical angle between diamond and glass is
(a) 52.50
(b) 770
(c) 370
(d) 55.50​

Answer 1

$\Large\underline{\underline{\sf \blue{Given}:}}$

• Refractive Index of diamond $\sf{\mu_d=\dfrac{5}{2}}$

• Refractive Index of Crown Glass $\sf{\mu_g=\dfrac{3}{2}}$

$\Large\underline{\underline{\sf \blue{To\:Find}:}}$

• Critical angle between diamond and glass $\sf{(\theta_c)}$=?

$\Large\underline{\underline{\sf \blue{Solution}:}}$

$\Large\underline{\underline{\sf \red{Remember}:}}$

Light travels from Denser medium to Rarer medium .

$\large{\boxed{\sf Critical\:Angle(sin\:\theta_c)=\frac{\mu_g}{\mu_d} }}$

$\implies{\sf \dfrac{\dfrac{3}{2}}{\dfrac{5}{2}}}$

$\implies{\sf \dfrac{3}{2}×\dfrac{2}{5}}$

$\implies{\sf sin\: \theta_c=\dfrac{3}{5}}$

We know that

sin 37° = $\sf{\dfrac{3}{5}}$

•°• $\implies{\sf sin\theta_c=37°}$

$\Large\underline{\underline{\sf \blue{Answer}:}}$

•°• Critical Angle between diamond and glass is 37°.