Suppose that light is incident on a double slit apparatus, with a slit separatio

Question

Suppose that light is incident on a double slit apparatus, with a slit separation d, at an angle of to the normal (see illustration). (a) Derive an equation in terms of the variables d, o, 0, integers m 0, t1, 2... or n 0, -1, t2... depending on what variable you'd like to represent integers!), and the wavelength A of the incoming light; that yields the location of the maxima (constructive interference in terms of the angle 0 (b) If 20%, what is the angle 6 of the m 0 central maximum? (c) If the wavelength of the incoming light is 500 x 10 9 m, the slit separation is 0.25 mm, and the distance to the screen is D 10 m, how far from the central (m 0) maximum is the nearest (m 1) maximum? (Show all work to receive full credit.)

Explanation / Answer

Here in the above figure

tan = y/D where y is distance between 2 consecutive maximas

For such small angles

tan is approximately equal to sin

Now condition for maxima is

dsin = m

max = dsin/m

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