Question

ACB is a right-angled glass prism with refractive index 1.5. Angle A, B, C are 60${}^{\circ }$,30 ${}^{\circ }$and 90${}^{\circ }$ respectively. A thin layer of liquid is on the AB. For a ray of light which is incident normally on AC to ;be totally reflected at AB, the refractive index of the liquid on AB should be

• A. 1.5
• B. 1.4
• C. 1.3
• D. 1.2

Answer 1

The correct option is C 1.3

Given, $\mu$=refractive index of liquid.

From figure it is itself clear that , angle of incidence, $i={60}^o$

Now, for internal reflection , angle of refraction $r={90}^o$

Now, $\frac{\sin i}{\sin r}=\frac{\mu }{{\mu }_1}$

$⟹\sin {60}^o=\frac{\mu }{1.5}$

$⟹\mu =\frac{\sqrt{3}}{2}\times 1.5$

$⟹\mu =1.3$

Hence, answer is option-(C)