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(D) Let $P$ be the point on the screen directly in front of slit $S_1$. The path difference between the light rays reaching $P$ from $S_1$ and $S_2$ i

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Both $(a)$ and $(c)$

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(D) Let $P$ be the point on the screen directly in front of slit $S_1$. The path difference between the light rays reaching $P$ from $S_1$ and $S_2$ is given by:$\Delta x = S_2P - S_1P = \sqrt{b^2 + d^2} - d$Using binomial expansion for $d >> b$:$\Delta x = d(1 + \frac{b^2}{d^2})^{1/2} - d \approx d(1 + \frac{b^2}{2d^2}) - d = \frac{b^2}{2d}$For destructive interference (missing wavelengths),the path difference must be an odd multiple of $\frac{\lambda}{2}$:$\Delta x = (2n - 1)\frac{\lambda}{2}$,where $n = 1, 2, 3, ...$Equating the two expressions for path difference:$\frac{b^2}{2d} = (2n - 1)\frac{\lambda}{2}$$\lambda = \frac{b^2}{(2n - 1)d}$For $n = 1$,$\lambda = \frac{b^2}{d}$.For $n = 2$,$\lambda = \frac{b^2}{3d}$.Thus,both $(a)$ and $(c)$ are correct.

In Young's double slit experiment,white light is used. The separation between the slits is $b$. The screen is at a distance $d$ $(d >> b)$ from the slits. Some wavelengths are missing exactly in front of one slit. These wavelengths are

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