Triple Slit Experiment#

A triple-slit experiment has a slit spacing \(d = 20 \rm{\mu m}\) and is illuminated by a laser of wavelength \(\lambda = 500 \rm{nm}\) and is a distance \(L = 10 \rm{cm}\) from a screen.

Part 1#

Without using the small angle approximation calculate the spacing between the \(m = 0\) and \(m = {{ params_m }} \) peaks.

Answer Section#

Please enter in a numeric value in \(\rm{mm}\).

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Part 2#

Without using the small angle approximation calculate the spacing between the \(m = 9\) and \(m = 10\) peaks.

Answer Section#

Please enter in a numeric value in \(\rm{mm}\).

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Part 3#

In the small angle approximation \(\tan(\theta) = \sin(\theta) = \theta\), where \(\theta\) is in radians. What is the spacing between the \(m = 0\) and \(m = {{ params_m }}\) peaks in the small angle approximation?

Answer Section#

Please enter in a numeric value in \(\rm{mm}\).

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Part 4#

What is the spacing between the \(m = 9\) and \(m = 10\) peaks in the small angle approximation?

Answer Section#

Please enter in a numeric value in \(\rm{mm}\).

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Part 5#

Based on your results in Parts 1-4 is the small angle approximation a good approximation for the spacing between the \(m = 0\) and \(m = {{ params_m }}\) peaks and the \(m = 9\) and \(m = 10\) peaks?

Answer Section#

  • It is a good approximation to the spacing between the \(m = 0\) and \( m = \) 2 peak, but not a great approximation to the spacing between the \(m = 9\) and \( m = 10\) peak as the angle for \(y_{10}\) is just outside the range of validity of the small angle approximation.

  • It is a good approximation to both spacings since the angles remain small out to \(m = 10\).

  • It is a not a good approximation either angle as one cannot meaningfully use the small angle approximation in diffraction problems even when the wavelength is small relative to the slit spacing.

Part 6#

If the colour of the laser changed to purple with a wavelength \(\lambda = 400 \rm{nm}\), how would the spacing change?

Answer Section#

  • The spacing between the maxima would increase.

  • The spacing between the maxima would not change.

  • The spacing between the maxima would decrease.

Attribution#

Problem is licensed under the CC-BY-NC-SA 4.0 license.
The Creative Commons 4.0 license requiring attribution-BY, non-commercial-NC, and share-alike-SA license.