In a double slit experiment the angular width of a fringe is found to be `0.2^(@)` on a screen placed I m away. The wavelength of light used in 600 nm. What will be the angular width of the fringe if the entire experimental apparatus is immersed in water ? Take refractive index of water to be `4//3`.

Explanation

Given, angular fringe width, `theta = 0.2^@`
Wavelength of light used in air,
`lambda_1 = 600 nm = 6 xx 10^(-7) m`
Refractive index of water, `mu = 4/3 = 1.33`
In air,
`theta = lambda/d`
In water,
The wavelength of light,
`lambda. = lambda/mu`
`:. ` Angular fringe width will become :
`theta. = (lambda.)/d = (lambda)/(mu d) = (theta)/(mu) = (0.2^@)/(1.33) = 0.15^@`.