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Question

A parallel beam of monochromatic light of wavelength 600 nm falls normally on a slit of width 0.5 mm. The resulting diffraction pattern is observed on a screen placed of 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
3 mm
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B
0.3 mm
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C
0.003 mm
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D
0.03 mm
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Solution

The correct option is B 0.3 mm
Given:
λ=600 nm; b=0.5 mm; D=50 cm

The angular position of the first minimum from the central maximum is given by,

bsinθ1=λsinθ1=λb

For small θsinθθ

θ1=λb

The angular position of the first maximum from the central maximum is given by,

bsinθ2=3λ2

θ2=3λ2b

Therefore, the angular separation between the first minimum and first maximum on the same side of the central maximum is given by,

Δθ=θ2θ1

Δθ=3λ2bλb=λ2b

Therefore, linear separation will be,

Δx=DΔθ=Dλ2b

Δx=0.5×600×1092×0.5×103

Δx=3×104 m=0.3 mm

Hence, option (C) is correct.

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