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Question
State with reason, how the linear width of the central maximum will be affected if
(i) monochromatic yellow light is replaced with red light, and
(ii) distance between the slit and the screen is increased.
Solution 1
sin θ =`lambda/a`
where θ is a very small
sin θ = θ
aθ = λ
θ `= lambda/a`
θ `= x/D`
`lambda /a = x/D`
`x = (lambdaD)/a`
width in of central maxima
ω = 2x
`omega = 2x = (2 lambdaD )/a`
(i) `omega = (2 lambda D)/a`
if yellow light replaced by red light its wavelength increases so width will also increase.
(ii) If distance between slit & screen increased width will increase
Solution 2
For a single slit experiment, the size(angular width) of the central maximum is given by `(2lambda)/"a"`, where a is the slit width.
So the width of the central maximum is directly proportional to the wavelength of light and inversely proportional to slit width.
(i) When monochromatic yellow light is replaced with monochromatic red light, the Width of the central maximum will increase, because the wavelength of red light is more than the wavelength of yellow light.
(ii) When the distance between the slit and the screen is increased, there is no effect on the width of the central maximum, as the width of the central maximum clearly depends only on wavelength and slit width, not on the distance of the screen from the slit.
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