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The number of waves in a glass slab of t...

The number of waves in a glass slab of thickness 4 cm is the same as in a water column of height 5 cm ,when the same monochromatic ray of light travels through them .what is the refractive index of water if the refractive index of glass is `(5)/(3)` ?

A

`1.25`

B

`1.5`

C

`1.33`

D

`1.75`

Text Solution

Verified by Experts

The correct Answer is:
C
Number of waves in a medium (N) = `("Thickness")/("Wavelength in the medium")`
`because N_("glass") = N_("water")`
`therefore (4)/(lambda_(g)) = (5)/(lambda_(w)) therefore (lambda_(g))/(lambda_(w)) = (4)/(5)`
but `lambda prop (1)/(R.I.) therefore (n_(w))/(n_(g)) = (lambda_(g))/(lambda_(w))`
`therefore n_(w) = n_(g) xx (lambda_(g))/(lambda_(w)) = (5)/(3) xx (4)/(5) = (4)/(3) = 1.33`
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