Question

In two separate Young's double-slit experimental set-ups and two monochromatic light sources of different wavelengths are used to get fringes of equal width. The ratios of the slits separations and that of the wavelengths of light used are 2:1 and 1:2 respectively. The corresponding ratio of the distances between the slits and the respective screens (D₁/D₂) is_______.}

Hint:

If you decrease the wavelength (making the fringes narrower), you must increase the screen distance or decrease the slit separation to maintain the same fringe width.

Answer 1

Correct Answer: 4

In Young's double-slit experiment, the fringe width (β) is given by: β = (λD)/d, where λ is the wavelength, D is the distance between slits and the screen, and d is the slit separation. Given two setups with equal fringe widths, we have λ₁D₁/d₁ = λ₂D₂/d₂. Let's denote:

1. The ratio of slit separations: d₁/d₂ = 2/1 = 2.

2. The ratio of wavelengths: λ₁/λ₂ = 1/2.

Substituting these into the fringe width equality:

(λ₁D₁)/d₁ = (λ₂D₂)/d₂.

We can rearrange to find the ratio of the distances D₁/D₂:

λ₁D₁d₂ = λ₂D₂d₁.

Substituting the given ratios (d₁/d₂ = 2 and λ₁/λ₂ = 1/2):

((1/2)D₁)d₂ = (1D₂)(2d₂).

D₁D₂ = 2D₂.

Therefore, D₁/D₂ = 4.

Finally, the computed ratio D₁/D₂ is 4, fitting perfectly within the specified range [4,4].