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Thus, to obtain destructive interference for a single slit ,
where is the slit width, is the light’s wavelength, is the angle relative to the original direction of the light, and is the order of the minimum. [link] shows a graph of intensity for single slit interference, and it is apparent that the maxima on either side of the central maximum are much less intense and not as wide. This is consistent with the illustration in [link] (b).
Visible light of wavelength 550 nm falls on a single slit and produces its second diffraction minimum at an angle of relative to the incident direction of the light. (a) What is the width of the slit? (b) At what angle is the first minimum produced?
Strategy
From the given information, and assuming the screen is far away from the slit, we can use the equation first to find , and again to find the angle for the first minimum .
Solution for (a)
We are given that , , and . Solving the equation for and substituting known values gives
Solution for (b)
Solving the equation for and substituting the known values gives
Thus the angle is
Discussion
We see that the slit is narrow (it is only a few times greater than the wavelength of light). This is consistent with the fact that light must interact with an object comparable in size to its wavelength in order to exhibit significant wave effects such as this single slit diffraction pattern. We also see that the central maximum extends on either side of the original beam, for a width of about . The angle between the first and second minima is only about . Thus the second maximum is only about half as wide as the central maximum.
A diffraction pattern is formed on a screen when light of wavelength 410 nm is passed through a single slit of width 1 μm. If the source light is replaced by another light of wavelength 700 nm, what should be the width of the slit so that the new light produces a pattern with the same spacing?
(d)
Monochromatic light passing through a single slit forms a diffraction pattern on a screen. If the second minimum occurs at an angle of 15º, find the angle for the fourth minimum.
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