Double Slit and Diffraction Grating Interference

00:00 10 marks

A scientist investigates the properties of light using a double-slit experiment and then a diffraction grating. Monochromatic light of wavelength 633 nm is used.

Part a

3 minutes 2 marks

Question

In the double-slit experiment, the slits are separated by 0.250 mm and the screen is placed 1.50 m away from the slits. Calculate the separation between adjacent bright fringes observed on the screen.
[2]

Hint Hint

Hint

Use the formula \(s = \frac{\lambda D}{d}\). Ensure all distances are in SI units (meters). \(\lambda = 633 \text{ nm}\), \(D = 1.50 \text{ m}\), \(d = 0.250 \text{ mm}\).

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3.80 × 10⁻³ m (or 3.80 mm)

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Part b(i)

4 minutes 3 marks

Question

The double-slit apparatus is now replaced with a diffraction grating that has 500 lines per mm. The light is incident normally on the grating.
(i) Calculate the angle at which the second-order maximum is observed.
[3]

Hint Hint

Hint

First, calculate the grating spacing \(d\) from the number of lines per mm. Then use the grating equation \(n\lambda = d \sin\theta\) with \(n=2\).

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39.3°

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Part b(ii)

4 minutes 3 marks

Question

(ii) Determine the total number of maxima that can be observed.
[3]

Hint Hint

Hint

Find the maximum possible integer order \(n_{max}\) using the condition \(\sin\theta \le 1\) in the grating equation. The total number of maxima is \(2n_{max} + 1\).

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Part c

4 minutes 2 marks

Question

The monochromatic light source is replaced by a source emitting two wavelengths, 633 nm and 488 nm. Describe the appearance of the pattern observed on the screen using the diffraction grating compared to using only the 633 nm light.
[2]

Hint Hint

Hint

Consider how the grating equation \(n\lambda = d \sin\theta\) relates the angle \(\theta\) to the wavelength \(\lambda\) for a fixed order \(n\) and grating spacing \(d\). How will the patterns for the two wavelengths appear relative to each other?

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Complete Answer

Two superimposed sets of maxima are observed. For n>0, the 488 nm maxima are at smaller angles than the 633 nm maxima.

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