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  • The refractive index of a medium  with respect to a medium is <img alt="2/3" src="https://learn

The refractive index of a medium 'x' with respect to a medium 'y' is 2/3 and the refractive index of medium 'y'with respect to medium'z' is 4/3. Find the refractive index of medium 'z' with respect to medium 'x'. If the speed of light in medium 'x' is 3\times 10^{8}\; ms^{-1}, calculate the speed of light in medium'y'.
Option: 1
Option: 2
Option: 3
Option: 4

Answers (1)

(I) Z/X=?

X/Y=2/3

Y=3X/2...(1)

Y/Z=4/3

Y=4Z/3...(2)

Equate RHS of (1) and (2)

3X/2=4Z/3

9X=8Z

Therefore, Z/X=9/8.

Hence, refrective index of medium Z w.r.t medium X is 9/8.

(II)Let speed of light in medium 'Y' be 'V'

Let speed of light in medium 'X' be 'C' i.e. 3*10^8m/s

So, Y/X=3/2...(3)

C/V=3*10^8/V...(4)

Equate RHS of (3) and (4)

3/2=3*10^8/V

So, 3V=3*10^8*2

Therefore, V=3*10^8*2/3

V=10^8*2

Therefore, V=2*10^8m/s

Hence, speed of light in medium Y is 2*10^8m/s

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