Question

The speed of light in media ' $A$ ' and ' $B$ ' are $2.0 \times$ $10^{10} cm / s$ and $1.5 \times 10^{10} chm / s$ respectively. A ray of light enters from the medium $B$ to $A$ at an incident angle ' $\theta$ '. If the ray suffers total internal reflection, then

• A. $\theta=\sin ^{-1}\left(\frac{3}{4}\right)$
• B. $\theta >\sin ^{-1}\left(\frac{2}{3}\right)$
• C. $\theta< \sin ^{-1}\left(\frac{3}{4}\right)$
• D. $\theta >\sin ^{-1}\left(\frac{3}{4}\right)$

Answer 1

Answer: (D)

$\sin i _{ c }=\frac{ n _{ r }}{ n _{ d }}=\frac{ C _{ d }}{ C _{ r }}=\frac{1.5 \times 10^{10}}{2 \times 10^{10}}$

$\sin i_{c}=\frac{3}{4}$
$i_{c}=\sin ^{-1}\left(\frac{3}{4}\right)$
for T I R $ \theta>i_{c}$
$\theta>\sin ^{-1}\left(\frac{3}{4}\right)$