What happens to the intensity of central frinze in diffraction when we double the width of slit
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The size of the central maximum is given by 2λa2λa where a is the slit width.
It is clear if a is doubled, size of the central maximum is halved. However the intensity changes because of two factors.
One, doubling the width of the slit causes twice the light energy fall on the screen as compared to that with the original width.
Two, the light energy is now squeezed into half of the area on the screen because the size of the central maximum is halved.
The two factors make the intensity four times
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