Angular width of central maximum in the Fraunhoffer diffraction pattern of a slit is measured. The slit is illuminated by light of wavelength `6000Å`. When the slit is illuminated by light of another wavelength, the angular width decreases by `30%`. Calculate the wavelength of this light. The same decrease in the angular width of central maximum is obtained when the original apparatus is immersed in a liquid. Find the refractive index of the liquid.

Explanation

A ngular width of central maximum`=(2lambda)/a`
`lambda_(1)=600 nm, theta_(1)=(2lambda_(1))/a …(i)`
`lambda_(2)=?, theta_(2)=theta_(1)xx0.7=(2lambda_(2))/a …(ii)`
(i)//(ii)
`1/0.7=lambda_(1)/lambda_(2)=600/lambda_(2)`
`lambda_(2)=420 nm`
When immersed in liquid, `lambda_(2)=lambda_(1)//mu`
`theta_(2)=theta_(1)xx0.7 ...(iii)`
`(2lambda_(1)//mu)/a=(2lambda_(1))/axx0.7`
(i)//(iii)
`1/0.7=mu implies mu=10/7=1.42`