A double slit is illuminated by light of wave length 6000 Å. The slit are 0.1 cm apart and the screen is placed one metre away. Calculate.
(i). The angular position of the `10^(th)` maximum in radian and
(ii). Separation of the two adjacent minimal.

Answer

(i) `6 xx 10^(-3) rad`. (ii) `6 xx 10^(-4) m`

Explanation

Here, `lambda = 6000 Å = 6 xx 10^(-7)m` ltbr. `d = 0.1 cm = 10^(-3), D = 1 m, n = 10`
`x = n lambda(D)/(d)`. If `theta` is angle of diffraction, then
`sin theta = (x)/(D) = (s lambda)/(d) = (10 xx 6 xx 10^(-7))/(10^(-3)) = 6 xx 10^(-3)`
As `sin theta` is small, `theta ~~ sin theta = 6 xx 10^(-3)rad`
(ii) Separation of two adjacent minima
`beta = (lambda D)/(d) = (6 xx 10^(-7) xx 1)/(10^(-3)) = 6 xx 10^(-4)m`