Diffraction

Diffraction#

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

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Useful Info#

When monochromatic light of wavelength λ passes through a double slit of separation d, constructive interference occurs at angles θm, where dsin⁡θm=mλ 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 asin⁡θp=pλ, 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=Ltan⁡θ. When the small angle approximation θ≈sin⁡θ≈tan⁡θ is valid (θ≪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, ai, for pattern (i) (use the small angle approximation if it applies). Express your answer in μm 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 μm.

Part 2#

Find the slit width, a_ii, for pattern (ii) (use the small angle approximation if it applies). Express your answer in μm 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 μm.

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.