The speed of light in media 'A' and 'B' are $2.0 \times 10^{10} \mathrm{~cm}/\mathrm{s}$ and $1.5 \times 10^{10} \mathrm{cm}/\mathrm{s}$ 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

(D) $\theta>\sin^{-1}\left(\frac{3}{4}\right)$

(A) $\theta=\sin^{-1}\left(\frac{3}{4}\right)$

(B) $\theta>\sin^{-1}\left(\frac{2}{3}\right)$

(C) $\theta<\sin^{-1}\left(\frac{3}{4}\right)$

JEE Main · 2022 · 29 Jun 2022 · Shift 2 · Geometrical Optics

The speed of light in media 'A' and 'B' are

2.0 \times 1 0^{10} cm / s

and

1.5 \times 1 0^{10} cm / s

respectively. A ray of light enters from the medium B to A at an incident angle '

θ

'. If the ray suffers total internal reflection, then

Answer: (D)

For total internal reflection from medium B (denser) to medium A (rarer), the critical angle is:

sin i_{c} = \frac{n _{A}}{n _{B}} = \frac{v _{B}}{v _{A}} = \frac{1.5 \times 1 0 ^{10}}{2.0 \times 1 0 ^{10}} = \frac{3}{4}

Therefore:

i_{c} = sin^{- 1} (\frac{3}{4})

For total internal reflection to occur, the incident angle must exceed the critical angle:

θ > i_{c} = sin^{- 1} (\frac{3}{4})

Answer: (D)

JEE Main · 2022 · 29 Jun 2022 · Shift 2 · Single correct option