In a double-slit experiment the angular width of a fringe is found to be `0.2^(@)` on a screen placed 1 m away. The wavelength of light used is 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

Angle `=("Arc")/("Radius")`
When above angle is very small, we can write
Angular width of fringe `("linear width of fringe")/(D)`
`:.theta=(beta)/(D)` (Where D = distance between slit and screen)
`:.theta=(lamdaD//d)/(D)`
`:.theta=(lamda)/(d)(" in air")" "......(1)`
`impliestheta.=(lamda.)/(d)` ( in water)
`:.theta.=(lamda//n)/(d)" "("":.n=(lamda)/(lamda.)implieslamda.=(lamda)/(n))`
`:.theta.=(1)/(n)((lamda)/(d))`
`:.theta.=(1)/(n)`
`=((0.2)^(@))/(4//3)`
`=(0.15)^(@)`