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:

a—> red
b—> green
c—> yellow
d—>green
e—>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