In a Young's double slit experiment, a student observes $8$ fringes in a certain segment of screen when a mono

Question

In a Young's double slit experiment, a student observes $8$ fringes in a certain segment of screen when a monochromatic light of $600	ext{ nm}$ wavelength is used. If the wavelength of light is changed to $400	ext{ nm}$, then the number of fringes he would observe in the same region of the screen is

Accepted Answer

The fringe width $\beta = \frac{\lambda D}{d}$. The number of fringes $n$ in a segment of length $L$ is $n = \frac{L}{\beta} = \frac{Ld}{\lambda D}$. Since $L, d, D$ are constant, $n \propto \frac{1}{\lambda}$. Thus, $n_1 \lambda_1 = n_2 \lambda_2$. $8 	imes 600 = n_2 	imes 400$, so $n_2 = \frac{4800}{400} = 12$.

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