Problem

In YDSE, if a bichromatic light having wavelengths

\lambda_1

and

\lambda_2

is used, then the maxima due to both lights will overlap at a certain distance

y

from the central maxima. Take separation between slits as

d

and distance between screen and slits as

D

. Then the value of

y

will be (1)

\left(\frac{\lambda_1 + \lambda_2}{2D}\right)d

(2)

\left(\frac{\lambda_1 - \lambda_2}{D}\right)2d

(3) LCM of

\frac{\lambda_1 D}{d}

and

\frac{\lambda_2 D}{d}

(4) HCF of

\frac{\lambda_1 D}{d}

and

\frac{\lambda_2 D}{d}

Intuitive explanation

The key insight is that maxima from different wavelengths occur at different positions, but they coincide when the path difference satisfies both wavelengths' constructive interference conditions simultaneously. You need to find where the $m_1$ -th bright fringe of $\lambda_1$ overlaps with the $m_2$ -th bright fringe of $\lambda_2$ —this happens when both path differences equal integer multiples of their respective wavelengths at the same location $y$ .

Intuitive explanation

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