You must design a pair of slits for a demonstration in which the first minimum of the diffraction pattern sits at the same place as the 5th order maximum of the interference pattern. What is the ratio of the slit spacing over the slit width? Recall that the light intensity at the screen is the product of the double slit interference pattern that corresponds to the slit spacing, and the single slit diffraction pattern that corresponds to the slit width.

Question

Physics

Elle Cook

24 February, 13:21

You must design a pair of slits for a demonstration in which the first minimum of the diffraction pattern sits at the same place as the 5th order maximum of the interference pattern. What is the ratio of the slit spacing over the slit width? Recall that the light intensity at the screen is the product of the double slit interference pattern that corresponds to the slit spacing, and the single slit diffraction pattern that corresponds to the slit width.

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Layne Rangel · Answer 1

Let the slit width be a and distance between slit is d.

slit width will give rise to diffraction pattern

first minima will be formed at

distance = λ D / a where λ is wave length of light and D is distance of screen.

Now, for interference pattern, fifth order maxima will be formed at

distance = 5λ D / d

Since they coincide each other

λ D / a = 5λ D / d

5 a = d

d / a = 5