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In a Fraunhofer single-slit diffraction experiment using light of wavelength lambda, the first minimum is formed at 37 deg. What is the direction of the first secondary maximum?

1. tan⁻¹(4/3)
2. sin⁻¹(3/4)
3. sin⁻¹(9/10)
4. tan⁻¹(3/4)

Correct answer: sin⁻¹(9/10)

Solution

The first minimum occurs at a*sin(37 deg) = lambda, giving a = lambda/(3/5) = 5*lambda/3. The first secondary maximum (between 1st and 2nd minima) occurs at a*sin(theta) = 3*lambda/2, so sin(theta) = 3*lambda/(2*(5*lambda/3)) = 9/10, i.e., theta = sin⁻¹(9/10).

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