Ray Optics

JEE Main level, single correct, medium

71 of 295

Question 71 of 295

Light is incident from a medium into air at two possible angles of incidence (A) 20∘20^{\circ} and (B) 40∘40^{\circ}. In the medium light travels 3.0 cm3.0 \mathrm{~cm} in 0.2 ns0.2 \mathrm{~ns}. The ray will :

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Answer: (B) suffer total internal reflection in case (B) only

Velocity of light in medium
Vmed =3 cm0.2 ns=3×10−2 m0.2×10−9 s=1.5 m/s\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
μ=Vair Vmed =3×1081.5=2 m/s\mu=\frac{V_{\text {air }}}{V_{\text {med }}}=\frac{3 \times 10^8}{1.5}=2 \mathrm{~m} / \mathrm{s}
As μ=1sin⁡C\mu=\frac{1}{\sin C}
∴sin⁡C=1μ=12=30∘\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)(i=40∘>30∘)(B)\left(i=40^{\circ}\gt 30^{\circ}\right) only.

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