Assume the figure below was photographed with red light of a single wavelength ?

Question

Assume the figure below was photographed with red light of a single wavelength ?0. The light passed through a single slit of width a and traveled distance L to the screen where the photograph was made. Consider the width of the central bright fringe, measured between the centers of the dark fringes on both sides of it. Rank from largest to smallest the widths of the central fringe in the following situations and note any cases of equality. (Use only ">" or "=" symbols. Do not include any parentheses around the letters or symbols.)
(a) The experiment is performed as photographed.
(b) The experiment is performed with light whose frequency is increased by 50%.
(c) The experiment is performed with light whose wavelength is increased by 50%.
(d) The experiment is performed with the original light and with a slit of width 2a.
(e) The experiment is performed with the original light and slit and with distance 2L to the screen.

Explanation / Answer

The formula that governs this is y/L = m(wavelength)/a

Also we need to know that v = f(wavelength) so frequency and wavelength are inversely proportional

So.

Option a) We have the original

Option b) When the frequency increases by 50% (up by a factor of 1.5), wavelength decreases by that much, and central bright will be smaller by a factor of 1.5

Option c) When wavelength is increased by 50%, which means up by a factor of 1.5, the central bright will increase by a factor of 1.5

Option d) The slit width doubles, the central bright will be cut in half, reduced by a factor of 2

Option e) The length to the screen doubles, the central bright doubles, increased by a factor of two

So, in order from largest to smallest, we have

Option e > Option c > Option a > Option b > Option d

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