Question

A glass plate 2.95 mmmm thick, with an index of refraction of 1.60, is placed between a point source of light with wavelength 600 nmnm (in vacuum) and a screen. The distance from source to screen is 1.25 cm. How many wavelengths are there between the source and the screen?

Answer 1

Answer:

$N_T=2086285.67$

Explanation:

Given;

Thickness of the glass plate, $x=2.95\times 10^{-3}\ m$

refractive index of the glass plate, $n=1.6$

wavelength of light source in vacuum, $\lambda=600\times 10^{-9}\ m$

distance between the source and the screen, $d=1.25\ m$

Distance travelled by the light from source to screen in vacuum:

$d_v=d-x$

$d_v=1.25-0.00295$

$d_v=1.24705\ m$

So the no. of wavelengths in the vacuum:

$N=\frac{d_v}{\lambda}$

$N=\frac{1.24705}{6\times 10^{-7}}$

$N\approx2.0784\times 10^{6}$  .......................(1)

Now we find the wavelength of the light wave in the glass:

$n=\frac{\lambda}{\lambda'}$

where:

$\lambda'=$ wavelength of light in the medium of glass.

$1.6=\frac{600\times 10^{-9}}{\lambda'}$

$\lambda'=375\times 10^{-9}\ m=375\ nm$

Now the no. of wavelengths in the glass:

$N'=\frac{x}{\lambda'}$

$N'=\frac{2.95\times 10^{-3}}{375\times 10^{-9}}$

$N'=7.8667\times 10^{3}$ ............................(2)

From (1) & (2):

• total no. of wavelengths are there between the source and the screen:

$N_T=N+N'$

$N_T=2086285.67$