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. ${90}^o$
• B. ${45}^o$
• C. ${68}^o$
• D. ${66}^o$
• E. ${24}^o$

Answer 1

The correct option is E ${24}^o$

Given : $n_a=1.00$ $n_d=2.42$

For total internal reflection to occur, the incidence angle must be greater than the critical angle.

Critical angle of diamond $\theta =si{n}^{-1}(\frac{n_a}{n_d})$ $=si{n}^{-1}(\frac{1.00}{2.42})={24}^o$

Thus the smallest angle for total internal reflection to occur in diamond is ${24}^o$.