Question

In a YDSE, the screen is rotated by 60∘ about an axis parallel to the slits. The slit's separation is 3 mm, slit to screen distance (at central fridge) is 4 m and wavelength of light is 450 nm. The separation between the 3rd dark fringe on the both side of the central fringe is

A
6 mm
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B
8 mm
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C
43 mm
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D
23 mm
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Solution

The correct option is A 6 mmGiven, d=3 mm ; D=4 mλ=450 nm ; θ=60∘ In YDSE, nth position of dark fringe is given by, yn=(2n−1)2λDd For 3rd dark fringe, y3=52λDd=52×450×10−9×43×10−3=1.5 mm From the diagram, y′=ycosθ=ycos60∘=2y ∴y′=2×1.5=3 mm The total distance between the 33rd dark fridge on both sides is, d′=2y′=6 mm <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, (A) is the correct answer.

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