A diffraction grating 22.0mm wide has 6000 rulings. Light of wavelength 592nm is

ID: 1313903 • Letter: A

Question

A diffraction grating 22.0mm wide has 6000 rulings. Light of wavelength 592nm is incident perpendicular on the grating.

a.) What is the largest value of theta at which maxima appear on a distant viewing screen?

Range for a Correct Answer: 74.466 to 76.734 degrees

b.) What is the second largest angle at which maxima appear on a distant viewing screen?

Correct Answer: 52.993 to 54.607 degrees

c.) What is the third largest angle at which maxima appear on a distant viewing screen?

Correct Answer: 39.597 to 40.803 degrees

How do I do these? I think I am using the wrong m value. When I did part a I used m=5 and got 53.83 degrees which is wrong.

a) so d = 22.0E-3/6000

so to find max m, set theta = 90

m lambda = d

mmax = d/lambda= (22.0E-3/6000)/592.0E-9=6.19

so max m is 6

so m lambda = d sin theta

theta = arcsin(6*592.0E-9/(22.0E-3/6000))=75.63 degrees

b) now m = 5

theta = arcsin(5*592.0E-9/(22.0E-3/6000))=53.83 degrees

c) now m = 4

theta = arcsin(4*592.0E-9/(22.0E-3/6000))=40.23 degrees

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