22: Problem 22.9

INTRO:
A 4.0-cm-wide diffraction grating has 2000 slits. It is illuminated by light of wavelength 590nm .

Part A:
What is the angle (in degrees) of the first diffraction order?
Express your answer to three significant figures and include the appropriate units.

SOLUTION:
givens: 
width = 4 cm
d = 4 cm / 2002 spaces between slits = 1.998⋅10^-3 cm
N = 2000
λ = 590 nm
m = 1

the angle can be determined by using the formula θ=m⋅λ/d
θ= 590 nm / 1.998⋅10^-3 cm
θ= 0.02953 radians = 1.69°

Part B:
What is the angle (in degrees) of the second diffraction order?
Express your answer to three significant figures and include the appropriate units.

SOLUTION:
do the same thing but with m=2
θ=2⋅590 nm / 1.998⋅10^-3 cm
θ= 0.05906 radians = 3.38°