Question

A ray of light is incident from a denser to a rarer medium. The critical angle for total internal reflection is ${\theta }_{\text{iC}}$ and Brewster's angle of incidence is ${\theta }_{\text{iB}}$ , such that $\frac{\text{sin}{\theta }_{\text{iC}}}{\text{sin}{\theta }_{\text{iB}}}=\eta =1\text{.}28$ . The relative refractive index of the two media is

• A. $\text{0.4}$
• B. $\text{0.2}$
• C. $\text{0.9}$
• D. $\text{0.8}$

Answer 1

Answer: (D)

${\mu }_1:$ refractive index of rarer medium
${\mu }_2:$ retractive index of denser medium
$sin{\theta }_C=\frac{{\mu }_1}{{\mu }_2}$
$tan{\theta }_B=\frac{{\mu }_1}{{\mu }_2}$
$sin{\theta }_C=tan{\theta }_B$
$\frac{sin{\theta }_C}{sin{\theta }_B}=\frac{tan{\theta }_B}{sin{\theta }_B}=\frac{1}{cos{\theta }_B}=1.28$
$\tan {\theta }_B=\frac{{\mu }_1}{{\mu }_2}=\frac{\sqrt{1-{\left(\frac{1}{1.28}\right)}^2}}{\left(\frac{1}{1.28}\right)}$
$=0.8$