In Young's double slit experiment, yellow light of wavelength 640 mm produces fringes of width 0.8 mm. What will be the fringe width if the light source is replaced by another monochromatic source of wavelength 720 mm and the separation between the slits is made thrice?

0.3 mm

The correct answer is Option (3) → 0.3 mm

In Young's double slit experiment,

fringe width, $β=\frac{λD}{d}$

Now,

$β_1=\frac{λ_1D}{d_1}$ and $β_2=\frac{λ_2D}{d_2}=\frac{λ_2D}{3d_1}$

$∴\frac{β_2}{β_1}=\frac{λ_2}{λ_1}×\frac{1}{3}$

$⇒β_2=\frac{λ_2}{λ_1}×\frac{1}{3}×β_1$

$=\frac{720}{640}×\frac{1}{3}×9.88=0.3mm$