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.

Hint

Hint

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Diffraction from multiple slits (two, three, four, ..., diffraction grating) shows constructive interference (bright peaks) when the path length difference $\Delta r = d\sin(\theta_m) = m\lambda$, where $m$ (an integer) is the order of the diffraction maximum, $\theta_m$ is the angle relative to the normal vector defining the plane of the slits, and $\lambda$ is the wavelength of the light. To find the distance of the $m^{\text{th}}$ order diffraction maximum from the central maximum on a screen a perpendicular distance $L$ from the slits, one can write $y_m = L\tan(\theta_m)$.

Close

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 \(\rm{mm}\).

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 \(\rm{mm}\).

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 \(\rm{mm}\).

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 \(\rm{mm}\).

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 \( m = \) 1 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.