Diffraction

Diffraction#

Photographs of the diffraction of a red laser of wavelength \(\lambda = 650\) nm are shown in figures (i) and (ii). A line of length \(7\) cm indicates the length scale on the screen.

../../../../../../_images/gratings3.png

Useful Info#

When monochromatic light of wavelength \(\lambda\) passes through a double slit of separation \(d\), constructive interference occurs at angles \(\theta_m\), where \(d\sin\theta_m = m\lambda\) and \(m = {0, 1, 2, ...}\) is an integer. This same relation holds true for light passing through a diffraction grating. Light passing through a single slit will destructively interfere at angles \(a\sin\theta_p = p \lambda\), where \(p = {1, 2, 3, ..}\) is a non-zero integer and \(a\) is the slit width. If a screen is placed at a distance \(L\) behind the slit(s)/grating, bright and dark lines are observed at a distance \(y\) from the central maximum given by \(y = L\tan\theta\). When the small angle approximation \(\theta \approx \sin\theta \approx \tan\theta\) is valid (\(\theta \ll 1\) expressed in radians), one expects a double-slit pattern to display equally spaced bright maxima, whereas a single-slit pattern exhibits a central maximum that is twice as wide as the subsequent maxima.

Part 1#

Find the slit width, \(a_i\), for pattern (i) (use the small angle approximation if it applies). Express your answer in \(\mu\)m to three significant figures. Take the distance you measured on Fig. (i) in Part 2 to be 1.00 cm, and the distance to the screen to be 60.0 cm.

Answer Section#

Please enter in a numeric value in \(\mu\)m.

Part 2#

Find the slit width, \(a\_{ii}\), for pattern (ii) (use the small angle approximation if it applies). Express your answer in \(\mu\)m to three significant figures. Take the distance you measured on Fig. (ii) in Part 2 to be 2.30 cm, and the distance to the screen to be 60.0 cm.

Answer Section#

Please enter in a numeric value in \(\mu\)m.

Part 3#

Do your answers to part 1 and 2 make sense in terms of which pattern indicated has the larger slit width?

Answer Section#

  • Yes, because the wider patterm should come from the larger slit width.

  • Yes, because the less wide pattern should come from the larger slit width.

  • No, because the wider pattern should come from the larger slit width.

  • No, because the less wide pattern should come from the larger slit width.

  • There is no relation between slit width and width of the pattern.

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.