In two separate Young's double-slit experimental set-ups and two… — Solution | JEE Physics

NVAEasyJEE 2026Interference (Young's Experiment)

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 ( $D_1/D_2$ ) is _____.

Answer

Correct answer:4

Step-by-step solution

Standard Method

Given: Fringe widths in the two YDSE set-ups are equal. Also, $d_1/d_2 = 2/1$ and $\lambda_1/\lambda_2 = 1/2$ .

Find: The ratio $D_1/D_2$ .

Using the fringe width relation:

\beta = \frac{\lambda D}{d}

Since the fringe widths are equal,

\frac{\lambda_1 D_1}{d_1} = \frac{\lambda_2 D_2}{d_2}

Rearranging,

\frac{D_1}{D_2} = \left(\frac{\lambda_2}{\lambda_1}\right) \left(\frac{d_1}{d_2}\right)

Now,

\frac{\lambda_2}{\lambda_1} = \frac{2}{1}, \qquad \frac{d_1}{d_2} = \frac{2}{1}

Therefore,

\frac{D_1}{D_2} = 2 \times 2 = 4

Hence, the required ratio is $4$ .

Common mistakes

Using the fringe width formula incorrectly as $\beta \propto d$ instead of $\beta \propto 1/d$ . This reverses the effect of slit separation. Always use $\beta = \frac{\lambda D}{d}$ .
Substituting $\lambda_1/\lambda_2 = 1/2$ directly in place of $\lambda_2/\lambda_1$ after rearrangement. Once the equation is solved for $D_1/D_2$ , take the reciprocal carefully before substituting.
Forgetting that equal fringe width means $\beta_1 = \beta_2$ and not comparing only wavelengths or only slit separations. Use the complete relation involving $\lambda$ , $D$ , and $d$ together.

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