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Question

A parallel beam of monochromatic light of wavelength 5000A is incident on a single narrow slit of width 0.001mm. The light is focused by a convex lens on a screen placed on a focal plane. The first minimum will be formed for the angle of diffraction equal to


A

50°

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B

15°

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C

20°

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D

30°

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Solution

The correct option is D

30°


Step 1: Given data

Wavelength of light, λ=5000A°

Slit width, d=0.001mm

Step 2: To find

The angle of diffraction in which the first minimum will be formed.

Step 3: Formula used

dsinθ=nλ

where d is the slit width, λ is the wavelength of light and n is the nth minima.

Step 4: Calculation for the angle:

Here since the first minimum is considered, n=1

dsinθ=nλ

Substituting the values,

dsinθ=nλsinθ=nλdsinθ=1×5000×10-100.001×10-3sinθ=12θ=sin-112θ=30°

The first minimum will be formed for the angle of diffraction equal to 30°

Option D is correct


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