Question

A young's double slit apparatus has slits separated by 0.28 mm and a screen 48 cm away from the slits. The whole apparatus is immersed in water and the slits are illuminated by the red light ($\lambda =700$ nm in vacuum) find th efringe-width of the pattern formed on the screen.

Answer 1

Given that: $d=0.28mm=0.28\times {10}^{-3}m,D=48cm,{\lambda }_a=700nminvaccum$
Let ${\lambda }_w$ = wavelength of red light in water
Since, $m=\frac{v_a}{v_w}=\frac{{\lambda }_a}{{\lambda }_w}=\frac{4}{3}$
$\Rightarrow \frac{3{\lambda }_a}{4}=\frac{3\times 700}{4}=525nm$
Wo, th efringe width of the pattern is given by,
$B={\lambda }_{w}D=\frac{525\times {10}^{-9}\times \left(0.48\right)}{\left(0.28\right)\times {10}^{-3}}=9\times {10}^{-4}=0.90mm$