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Physics Question on Ray optics and optical instruments

Time taken by light to travel in two different materials AA and BB of refractive indices μA\mu_{ A } and μB\mu_{ B } of same thickness is t1t _1 and t2t _2 respectively If t2−t1=5×10−10st_2-t_1=5 \times 10^{-10} s and the ratio of μA\mu_{ A } to μB\mu_{ B } is 1:21: 2 Then the thickness of material, in meter is: (Given vAv_A and vBv_B are velocities of light in AA and BB materials respectively)

A

5×10−10vam5 \times 10^{-10} v _{ a } m

B

5×10−10m5 \times 10^{-10} m

C

1.5×10−10m1.5 \times 10^{-10} m

D

5×10−10vBm5 \times 10^{-10} v _{ B } m

Answer

5×10−10vam5 \times 10^{-10} v _{ a } m

Explanation

Solution

The thickness of material\text{The thickness of material} :

thickness=5×10−10×VAVBVA−VBthickness = \frac{5 \times 10^{-10}\times V_AV_B}{V_A-V_B}

or  thickness=5×10−10×VAor \; thickness = 5 \times10^{-10}\times{ V_A}

The correct option is (A):\text{The correct option is (A):} 5×10−10vam5 \times 10^{-10} v _{ a } m