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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 $3.0 \mathrm{~cm}$ in $0.2 \mathrm{~ns}$. The ray will :
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Verified Answer
The correct answer is:
suffer total internal reflection in case (B) only
suffer total internal reflection in case (B) only
Velocity of light in medium
$$
\mathrm{V}_{\text {med }}=\frac{3 \mathrm{~cm}}{0.2 \mathrm{~ns}}=\frac{3 \times 10^{-2} \mathrm{~m}}{0.2 \times 10^{-9} \mathrm{~s}}=1.5 \mathrm{~m} / \mathrm{s}
$$
Refractive index of the medium
$$
\mu=\frac{V_{\text {air }}}{V_{\text {med }}}=\frac{3 \times 10^8}{1.5}=2 \mathrm{~m} / \mathrm{s}
$$
As $\mu=\frac{1}{\sin C}$
$$
\therefore \sin \mathrm{C}=\frac{1}{\mu}=\frac{1}{2}=30^{\circ}
$$
Condition of TIR is angle of incidence i must be greater than critical angle. Hence ray will suffer TIR in case of $(B)\left(i=40^{\circ}>30^{\circ}\right)$ only.
$$
\mathrm{V}_{\text {med }}=\frac{3 \mathrm{~cm}}{0.2 \mathrm{~ns}}=\frac{3 \times 10^{-2} \mathrm{~m}}{0.2 \times 10^{-9} \mathrm{~s}}=1.5 \mathrm{~m} / \mathrm{s}
$$
Refractive index of the medium
$$
\mu=\frac{V_{\text {air }}}{V_{\text {med }}}=\frac{3 \times 10^8}{1.5}=2 \mathrm{~m} / \mathrm{s}
$$
As $\mu=\frac{1}{\sin C}$
$$
\therefore \sin \mathrm{C}=\frac{1}{\mu}=\frac{1}{2}=30^{\circ}
$$
Condition of TIR is angle of incidence i must be greater than critical angle. Hence ray will suffer TIR in case of $(B)\left(i=40^{\circ}>30^{\circ}\right)$ only.
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