Question

The index of refraction for diamond is $2.42$. For a diamond in the air (index of refraction $=1.00$), what is the smallest angle that a light ray inside the diamond can make with a normal and completely reflect back inside the diamond (the critical angle)?

• A. ${90}^{\circ }$
• B. ${45}^{\circ }$
• C. ${68}^{\circ }$
• D. ${66}^{\circ }$
• E. ${24}^{\circ }$

Answer 1

The correct option is E ${24}^{\circ }$

For a light ray incident on the air-diamond surface to completely reflect back of the smallest possible angle is
$\mu sin{i}_{min}=1$

$⟹i_{min}=si{n}^{-1}\left(\frac{1}{\mu }\right)$

$=si{n}^{-1}\left(\frac{1}{2.42}\right)={24}^{\circ }$