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A slit of width a is illuminated by white light. What is the wavelength lambda of the light whose first side diffraction maximum is at 15^(@), thus coinciding with the first minimum for the red light? |
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Answer» Solution :KEY IDEA The first side maximum for any wavelength is about halfway between the first and second MINIMA for that wavelength. Calculations: Those first and second minima can be located with Eq. 35-57 by setting m = 1 and m = 2, respectively. Thus, the first side maximum can be located approximately by setting m = 1.5. Then Eq. 35-57 BECOMES `asin theta=1.5 lambda.`. Solving for `lambda.` and substituting known data yield `lambda.=(a sin theta)/(1.5)=((2511 nm)(sin 15^(@)))/(1.5)` = 430 nm. (Answer) Light of this wavelength is violet (FAR blue, near the short- wavelength limit of the HUMAN range of visible light). From the two equations we used, can you see that the first side maximum for light of wavelength 430 nm will always coincide with the first minimum for light of wave- length 650 nm, no matter what the slit width is? However, the angle `theta` at which this overlap occurs does depend on slit width. If the slit is relatively narrow, the angle will be relatively large, and conversely. |
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