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In Young’s double slit experiment the separation d between the slits is 2 mm, the wavelength λ of the light used is 5896 Å and distance D between the screen and slits is 100 cm. It is found that the angular width of the fringes is 0.20°. To increase the fringe angular width to 0.21° (with same λ and D) the separation between the slits needs to be changed to

1. 1.8 mm
2. 1.9 mm
3. 1.7 mm
4. 2.1 mm

Correct answer: 1.9 mm

Solution

The angular width of the fringes is given by θ = λ/d. To increase θ from 0.20° to 0.21°, the slit separation d must decrease. Using the ratio θ₁/θ₂ = d₂/d₁, we find d₂ = d₁ * (θ₁/θ₂) = 2 mm * (0.20°/0.21°) = 1.9 mm.

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