THE PROBLEM Light passes through three equally-spaced slits and then arrives at

Question

THE PROBLEM Light passes through three equally-spaced slits and then arrives at a screen. The first minimum occurs at an angle of 1 4 degrees. a) Calculate the angular position of the next minimum. (b) Calculate the angular position of the next maximum. PAPER SOLUTION Solve the problem on paper first, including all four IDEA steps. You will become a better physicist that way! Have you finished your paper solution already? Oyes Ono INTERPRET Identify all of the true statements. A. There will be a minimum at the center of the screen. B. There will be 2 minima for every maximum. C. There will be 3 minima for every maximum. D. Maxima and minima will alternate across the screen. E. None of the above. DEVELOP In your answers below, type c to represent O (a) Derive an algebraic expression for the angular position of the next minimumm (b) Derive an algebraic expression for the angular position of the next maximum.

Explanation / Answer

In case of multiple slits (diffraction grating), the maxima occurs when dsin? = m?.........(1), where

d = spacing between the screen and slits, ? = angular position, m = rank of maxima/minima and ? = wavelength of light

Since given that first minima occurs at angle ? = 4 degrees, from (1) we have, d * sin4 = 1 * ?

Or ? = d (sin4)..............(2)

So, using (2), angular position of next maximum (say ?3) is expresed as,

d * sin?3 = 3 * ? = 3 * d (sin4)....(assuming the first maxima at m = 0 and since one maxima has two minima, hence the next maxima should appear at m = 3)

Or, sin?3 = 3 * sin4

Or, ?3 = 12.08 degree (approx)

Similarly, angular position of next minimum (say ?2) can be derived as,

d * sin?2 = 3 * ? = 2 * d (sin4).....(assuming the first maxima at m = 0 and as first minima occurs at m = 1, hence next minima should appear at m = 2 as one maxima has two minima)

Or, sin?2 = 2 * sin4

Or, ?2 = 8.02 degree (approx)

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