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Question

A parallel beam of monochromatic light of wave length 600 nm, falls normally on a slit of width 0.5 mm. The resulting diffraction pattern is observed on a screen, placed 50 cm from the slit. The linear separation between the first minimum and the first maximum on the same side of the central maximum is,

A
0.3 mm.
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B
0.003 mm.
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C
3 mm.
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D
0.03 mm.
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Solution

The correct option is A 0.3 mm.
For first minimum, (a = width of the slit)
asinθ1=λ
sin θ1=λaθ1=λa(λ<<a)

Similarly, for first maximum,
asinθ2=3λ2θ2=3λ2a

Angular separation between them is,
Δθ=θ2θ1=3λ2aλa=λ2a

Linear separation between them is,
Δx=DΔθ=Dλ2a
=0.5×(600×109)2×(0.5×103)=0.3 mm.

Hence, (C) is the correct answer.

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