A ray of light entering from air into a denser medium of refractive index , as shown in figure. The light ray suffers

Question

A ray of light entering from air into a denser medium of refractive index $\frac{4}{3}$ , as shown in figure. The light ray suffers total internal reflection at the adjacent surface as shown. The maximum value of angle $θ$ should be equal to:

Smart Achievers · Accepted Answer

(1)

At maximum angle $θ$ ray at point B goes in grazing emergence, at all less values of $θ$ , TIR occurs. At point B $\frac{4}{3} \sin θ'' = 1 \times \sin 90 °$
$θ'' = \sin^{- 1} (\frac{3}{4})$

$θ' = (\frac{π}{2} - θ'')$

At point A $1 \times \sin θ = \frac{4}{3} \sin θ'$

$\sin θ = \frac{4}{3} \sin (\frac{π}{2} - θ'')$

$\sin θ = \frac{4}{3} \cos [\cos^{- 1} \frac{\sqrt{7}}{4}]$

$\sin θ = \frac{4}{3} \times \frac{\sqrt{7}}{4}$

$θ = \sin^{- 1} (\frac{\sqrt{7}}{3})$

Solution

Q.
A ray of light entering from air into a denser medium of refractive index $\frac{4}{3}$ , as shown in figure. The light ray suffers total internal reflection at the adjacent surface as shown. The maximum value of angle $θ$ should be equal to:

1 $\sin^{- 1} (\frac{\sqrt{7}}{3})$

2 $\sin^{- 1} (\frac{\sqrt{5}}{4})$

3 $\sin^{- 1} (\frac{\sqrt{7}}{4})$

4 $\sin^{- 1} (\frac{\sqrt{5}}{3})$

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Solution

Q. A ray of light entering from air into a denser medium of refractive index 43, as shown in figure. The light ray suffers total internal reflection at the adjacent surface as shown. The maximum value of angle θ should be equal to:

1 sin-1(73)

2 sin-1(54)

3 sin-1(74)

4 sin-1(53)