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  3. Physics
  4. Light is incident from a medium into air at two possible angles of incidence (A) 20° and (B) 40°. In the medium light travels 3.0 cm in 0.2 ns. The ray will :

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Q. Light is incident from a medium into air at two possible angles of incidence $(A) 20^{\circ}$ and $(B) 40^{\circ}$. In the medium light travels $3.0 \,cm$ in $0.2\, ns$. The ray will :

JEE MainJEE Main 2013Ray Optics and Optical Instruments

Solution:

Velocity of light in medium
$V_{med} = \frac{3\,cm}{0.2ns} = \frac{3\times10^{-2}m}{0.2\times10^{-9}s} = 1.5\,m/s$
Refractive index of the medium
$\mu = \frac{V_{air}}{V_{med}} = \frac{3\times10^{8}}{1.5} = 2\, m/s$
As$\,\mu = \frac{1}{sin\,C}$
$\therefore \,sin\,C = \frac{1}{\mu} = \frac{1}{2} = 30^{\circ}$
Condition of TIR is angle of incidence i must be greater than critical angle. Hence ray will suffer TIR in case of $\left(B\right) \left(i = 40^{\circ} > 30^{\circ}\right)$ only.