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Please show all work. Thanks. (I believe the diagram is marked 80cm for the distances of a, b, c, and d...) HY162 Exam 4 ay 2017 Name (20 pts) A two color laser emits a single beam of light that is a mixture of two different colors, 660 to our eye. 1. nm red and 540 nm green. These two colors mixed together appear yellow 80.6 cm two color lasex mixed bee m ?. qrati Scceen The laser beam passes through a transmission diffraction grating as shown. What are the colors (red, green, or yellow) of the spots on the screen? Spots are labeled as follows: a) b) c) d) e) f) if the diffraction grating has 2456 lines in 1.000 cm of width, show that the grating spacing is d = 4072 nm. g) What is the distance on the screen between points a and b? Solution for diffraction grating, d*sin(theta)=m*lambda where d=grating spacing theta=angle with the normal m=order of maximum lambda=wavelength so higher the wavelength, higher will be the distance from central spot. at the central spot, both the color will have a central bright fringe and hence their combination will appear as yellow. with green having lesser wavelength, it will have less distance from the central spot hence point b and d will be green and point a and e will be red. hence answers are: aâ€”> red bâ€”> green câ€”> yellow dâ€”>green eâ€”>red part f: grating spacing=total width/total number of lines =1 cm/2456 =4.0717*10^(-6) m =4071.7 nm ~ 4072 nm part g: first maxima for wavelength lambda will be at a distance of lambda*D/d where D=distance of screen from the grating=0.8 m d=grating spacing=4072 nm so for two different wavelengths lambda1 and lambda2, they will be at a distance of lambda1*D/d and lambda2*D/d so spacing between them=(lambda1-lambda2)*D/d using lambda1=660 nm and lambda2=540 nm we get spacing between a and b=0.023576 m =2.3576 cm .

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$Please show all work. Thanks. (I believe the diagram is marked 80cm for the distances of a, b, c, and d...) HY162 Exam 4 ay 2017 Name (20 pts) A two color laser emits a single beam of light that is a mixture of two different colors, 660 to our eye. 1. nm red and 540 nm green. These two colors mixed together appear yellow 80.6 cm two color lasex mixed bee m ?. qrati Scceen The laser beam passes through a transmission diffraction grating as shown. What are the colors (red, green, or yellow) of the spots on the screen? Spots are labeled as follows: a) b) c) d) e) f) if the diffraction grating has 2456 lines in 1.000 cm of width, show that the grating spacing is d = 4072 nm. g) What is the distance on the screen between points a and b? Solution for diffraction grating, d*sin(theta)=m*lambda where d=grating spacing theta=angle with the normal m=order of maximum lambda=wavelength so higher the wavelength, higher will be the distance from central spot. at the central spot, both the color will have a central bright fringe and hence their combination will appear as yellow. with green having lesser wavelength, it will have less distance from the central spot hence point b and d will be green and point a and e will be red. hence answers are:$

aâ€”> red
bâ€”> green
câ€”> yellow
dâ€”>green
eâ€”>red
part f:
grating spacing=total width/total number of lines
=1 cm/2456
=4.0717*10^(-6) m
=4071.7 nm
~ 4072 nm
part g:
first maxima for wavelength lambda will be at a distance of lambda*D/d
where D=distance of screen from the grating=0.8 m
d=grating spacing=4072 nm
so for two different wavelengths lambda1 and lambda2, they will be at a distance of
lambda1*D/d and lambda2*D/d
so spacing between them=(lambda1-lambda2)*D/d
using lambda1=660 nm and lambda2=540 nm
we get spacing between a and b=0.023576 m
=2.3576 cm

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