In the arrangement shown wavelength of light used is λ . The distance between slits S 1 and S 2 is d ( ≪ D ) . S 4 is on the axis of symmetry as shown. The distance between S 3 and S 4 is u

Question

In the arrangement shown wavelength of light used is $λ$ . The distance between slits $S_{1}$ and $S_{2}$ is $d (≪ D)$ . $S_{4}$ is on the axis of symmetry as shown. The distance between $S_{3}$ and $S_{4}$ is $u = \frac{λ D}{3 d}$ . If the ratio of maximum to minimum intensity observed on screen is k. Find k.

TestHub · Accepted Answer

If intensity of light incident on slits $S_{1}$ and $S_{2}$ is $I_{0}$ .

The intensity through $S_{4}$ will be $I_{1} = 4 I_{0}$

The intensity through $S_{3}$ will be $I_{2} = 4 I_{0} cos^{2} (ϕ /2) = I_{0}$

$k = \frac{I _{max}}{I _{min}} = (\frac{4 I _{0} + I _{0}}{4 I _{0} - I _{0}})^{2} = (\frac{3}{1})^{2} = \frac{9}{1}$

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JEE Advanced (2028)