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Question

(B) When two plane waves make a small angle $\alpha$ with each other,the interference pattern formed is equivalent to Young's Double Slit Experiment.T

Vedclass · Accepted Answer

$\frac{\lambda}{\alpha}$

Vedclass · Answer

(B) When two plane waves make a small angle $\alpha$ with each other,the interference pattern formed is equivalent to Young's Double Slit Experiment.The effective separation between the two virtual sources is $d$. If the waves are incident on a screen at a distance $D$,the angle between them is $\alpha = \frac{d}{D}$.The fringe width $\Delta x$ is given by the formula $\Delta x = \frac{\lambda D}{d}$.Substituting $d = D\alpha$ into the formula,we get $\Delta x = \frac{\lambda D}{D\alpha} = \frac{\lambda}{\alpha}$.However,for two plane waves interfering at an angle $\alpha$,the path difference changes as $\Delta x = \frac{\lambda}{\alpha}$ is the standard result for small angles. Given the provided options and standard physics conventions for this specific problem setup,the correct expression is $\Delta x = \frac{\lambda}{\alpha}$.

Two coherent plane light waves of equal amplitude make a small angle $\alpha (\alpha \ll 1)$ with each other. They fall almost normally on a screen. If $\lambda$ is the wavelength of the light waves,the fringe width $\Delta x$ of the interference pattern of the two sets of waves on the screen is:

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