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Waves and Particle Nature of Light

Single-slit patterns and the diffraction grating equation

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  • Papers 2 and 3

Overview

Recall questions on Huygens' construction, the single-slit pattern and how it changes with wavelength, and the grating equation with its slit spacing.

What you need to know

Answer each one before you reveal it.

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Numbers

Why can you hear someone talking round the corner of a doorway but not see them?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What is seen on a screen when monochromatic light passes through a single narrow slit?

    Model answer

    There is a wide, bright central maximum with much dimmer maxima on either side, separated by dark fringes, and the central maximum is about twice as wide as the others.

  2. 2

    How does the single-slit pattern change if red light is replaced by blue light of the same intensity?

    Model answer

    Blue light has a shorter wavelength so it diffracts less, and the whole pattern becomes narrower with the fringes closer together.

  3. 3

    Why can you hear someone talking round the corner of a doorway but not see them?

    Model answer

    Sound wavelengths of about a metre are comparable to the width of the doorway so the sound diffracts strongly, whereas light wavelengths of around 10⁻⁷ m are far smaller than the gap so light diffracts negligibly.

  4. 4

    What is a diffraction grating?

    Model answer

    It is a plate ruled with a very large number of equally spaced parallel slits or lines that diffract light and produce interference maxima.

  5. 5

    State the diffraction grating equation and say what each symbol represents:

    Model answer

    The equation is nλ = d sinθ, where n is the order of the maximum, λ is the wavelength, d is the spacing between adjacent slits and θ is the angle of the maximum from the straight-through direction.

  6. 6

    A grating is ruled with 300 lines per mm. What is the slit spacing d?

    Model answer

    The spacing is d = 1 ÷ (3.00 × 10⁵ lines per metre) = 3.33 × 10⁻⁶ m.

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