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(a) Show that a 30,000-line-per-centimeter grating will not produce a maximum for visible light. (b) What is the longest wavelength for which it does produce a first-order maximum?(c) What is the greatest number of lines per centimeter a diffraction grating can have and produce a complete second- order spectrum for visible light?
A. $=333.3 \mathrm{nm}$B. 333 $\mathrm{nm}$C. $N=6.58 \times 10^{3}$
Physics 103
Chapter 27
Wave Optics
Cornell University
University of Washington
University of Sheffield
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in about a first. We need to clear the slit separation. D uh, in once in the future we have, Ah, 30,000 lines. So 0.1 millimeters. You I 30,000 off. This gives us a D to be 3.33 times 10 to the power mine. A seven meter, which is 333.3 in enemy too. We knows the sine theta is equal to em, Linda, for the longest prevalent. Ah, Sign that. Ah, physical one and the m E report to one. Therefore d will be equal to London, which is 333.3 in enemy what would be the longest we have? A lentil MBA is equal to the slits Aggression Smith separation Mission RC to get the largest number off lines person to be true and still would produce a complete spectrum. We want the smallest slit separation that allows the longest prevalent off visible light to produce the second northern next month. So second order maximum well, the next moon So the Lambda Max lend a maximum will be equal to 7 69 meter, uh, or second order in musical too. And signing that icicle to one, so d So we do tear See part here. So D is it cool to to lambda maximum Ah, which is equal to two times off. 7 60 Nanami, Jerk. Excuse us. Um, 1.52 times 10 to the power minus seven meter. Then we can find the number off lines and bye. One line lying birdie that is equal to one divided by 1.52 guns tempted power minus seven tons, one meter divided by 1000 100 Son to meet you. So a disc use us the number of lines to be just write the result here, that is and to be 6.58 times 10 to the power, uh, three lines. So lines three lines person to meet you person do each year. So this this number of lines we have in a person to be true
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