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.

Answer

`4200 Å ; 1.43`

Explanation

(a) As angular width of central maximum is directly proportional to `lambda`. And angular width decreases by `30%`, thereofore, wavelength must have decreased by `30%`. The new wavelength would be `70%` of original wavelength.
`:. lambda' = (70)/(100) lambda = (7)/(10) xx 6000 Å = 4200 Å`
(b) When the apparatus is immersed in liquid, `lambda` changes to `lambda//mu`.
Angular width becomes `(1)/(mu)` times.
`:. (1)/(mu) = (70)/(100) or mu = (10)/(7) = 1.43`