JEE Main · 2022 · 25 Jun 2022 · Shift 1 · Geometrical Optics

The difference of speed of light in the two media

A

and

B

(v_{A} - v_{B})

2.6 \times 1 0^{7} m/s

. If the refractive index of medium

B

is 1.47, then the ratio of refractive index of medium

B

to medium

A

is: (Given: speed of light in vacuum

c = 3 \times 1 0^{8} ms^{- 1}

)

(A)1.303
(B)1.318
(C)1.13✓ Correct
(D)0.12

Answer: (C)

Solution

Using

v = \frac{c}{μ}

v_{B} = \frac{3 \times 1 0 ^{8}}{1.47} = 2.04 \times 1 0^{8} m/s

Given

v_{A} - v_{B} = 2.6 \times 1 0^{7} m/s

v_{A} = 2.04 \times 1 0^{8} + 2.6 \times 1 0^{7} = 2.3 \times 1 0^{8} m/s

Therefore,

μ_{A} = \frac{3 \times 1 0 ^{8}}{2.3 \times 1 0 ^{8}} = 1.304

The ratio

\frac{μ _{B}}{μ _{A}} = \frac{1.47}{1.304} \approx 1.13

JEE Main · 2022 · 25 Jun 2022 · Shift 1 · Single correct option

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