Question

A material is embedded between two glass plates. Refractive index $n$ of the material varies with thickness as shown below. The maxim um incident angle (in degrees) on the material for which beam will pass through the material is

• A. 60.0
• B. 53.1
• C. 43.5
• D. 32.3

Answer 1

Answer: (B)

Light beam passes through material, if no total internal reflection occurs at surface of material
$So,\sin i\le \frac{n_2}{n_1}$
$\Rightarrow \sin i\le \frac{1.2}{1.5}$
$\Rightarrow \sin i\le 0.8$
or $\sin \left(i_{\text{maximum}}\right)=0.8$
$\Rightarrow i_{\text{maximum}}=si{n}^{-1}\left(0.8\right)$
$\Rightarrow i_{\text{max}}=53.1^{\circ }$