Question

In youngs double slit experiment 62 fringes are seen in visible region for sodium light of wavelength 5893a of violet of wavelength 4358a is used in place of sodium light then the number of fringes seen will be

Answer 1

n1 = 62

w1 = 5893

w2 = 4358

total extent of fringes is constant for both wavelengths

i.e. n1w1D/d = n2w2D/d

n2 =62×5893/4358 = 84 (approx)

Answer 2

The number of fringes seen will be 84.

For sodium light,

Length of the region = No. of fringes × Fringe width

As fringe width = Dλ/d

As 'D' [distance between source and screen] and 'd' [distance between the slits] are constant throughout the experiment, so fringe width depends on λ, wavelength only.

λ = 5893A

No. of fringes = 62

∴ Length of the region = (5893 × 62) A

For violet light,

Length of the region is same as that for sodium light.

So, length of region = (5893 × 62) A

Wavelength of violet light = 4358 A

So, no. of fringes = (Length of region)/(Wavelength)

                             = (5893 × 62)/4358 = 83.8 ≈ 84

84 fringes are observed for violet light.