Question

A glass prism of refractive index $1.5$ is placed in water of refractive index $1.33$. The minimum value of the angle of the prism so that it will not be possible to have any emergent ray is :

• A. ${150}^{\circ }$
• B. ${125}^{\circ }$
• C. ${165}^{\circ }$
• D. ${180}^{\circ }$

Answer 1

Answer: (B)

${125}^{\circ }$

${\mu }_{prism}=$ $1.5$

${\mu }_{water}$ $=1.33$

${\mu }_r=\frac{1.5}{1.33}$

${\theta }_{cric}=si{n}^{-1}\left(\frac{1}{{\mu }_r}\right)=si{n}^{-1}\left(\frac{1.33}{1.5}\right)={62.5}^{\circ }$

Maximum possible angle A is given by: $A=2{\theta }_{cric}={125}^{\circ }$