Consider laser light passing through a single narrow slit. What happens to the w

Question

Consider laser light passing through a single narrow slit. What happens to the width of the central maximum of the diffraction pattern if the slit were now half as wide?  Use small angle approzimation to explain.

(Destructive interference for the first dark spot can be determined by the equations below. In the first equation, theta dark is the angle to the first dark fringe, lambda is the wavelength of laser light, and W is the slit width. In the second equation, y is the height of the first dark fringe and L is the distance from the slit to the screen.)

Explanation / Answer

Using small angle approzimation

W (theta) = lambda

theta = y/L

from above equations

lambda/W = y/L

y = L*lambda/W

if we half the width of slit then the width of the central maximum will increase.

The smaller the object the wave interacts with, the more spread there is in the interference pattern. Decreasing the size of the opening increases the spread in the pattern.

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