9.2 Single-Slit Diffraction

The formula for the position of the first minimum of the diffraction pattern produced by a single slit is given by:

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The frequency of monochromatic light passing through a slit is 2.44 × 10¹⁴ Hz. The screen is located 3.75 m from the single slit. The distance on the screen from the central maximum to the first minimum is 0.25 cm.

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Three diffraction patterns, x, y and z, are produced from three wavelengths of light, λ, 5λ and 10λ, passing through a slit of fixed width b. 

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The graph below shows the variation of light intensity, I with angular displacement θ on a screen placed far away from a narrow slit.

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Plane wavefronts of monochromatic light of wavelength λ are incident on a rectangular slit of width b. The light is brought to a focus after passing through the slit on a screen at a distance D from the slit as shown in the diagram below. 

The width of the slit is comparable to the wavelength of the light and b ≪ D. The point X on the screen is opposite the centre of the slit.  

The variation of the intensity incident on the screen with angle θ is shown on the graph below.

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In a single-slit diffraction experiment, the slit width is 0.030 mm and the wavelength of the light incident on the slit is 525 nm.

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The single slit of width b is replaced with rectangular slits, of width 2. The intensity distribution of a single slit is shown by the dotted line.

An experiment is set up where white light is incident on a single slit. 

(i)

Identify the first secondary maximum and the second diffraction minimum on the single slit intensity graph below.

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(ii)

Determine the wavelength of light for which the first secondary maximum occurs at an angle of 12°.

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A rectangular slit has width b and is comparable to the wavelength λ of plane wavefronts of monochromatic light incident upon it. After passing through the slit, the light is brought to a focus on a screen. 

The diagram shows a line normal to the plane of the slit, drawn from the centre of the slit to the screen is labelled PQ. The points X and Y are the first points of minimum intensity as measured from point Q. 

The diagram also shows two rays of light incident on the screen at point X. Ray RX leaves one edge of the slit and ray PX leaves the centre of the slit. The angle φ is small. 

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In a certain demonstration of single-slit diffraction λ = 400 nm, b = 0.12 mm, and the screen is a long way from the slit. 

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