Intense white light is incident on a diffraction grating that has 430 lines/mm.

Question

Intense white light is incident on a diffraction grating that has 430 lines/mm.

Intense white light is incident on a diffraction grating that has 430 lines/mm. What is the highest order in which the complete visible spectrum can be seen with this grating? (Enter 1 for first order, 2 for second order, etc.) Your response differs from the correct answer by more than 10%. Double check your calculations. What is the angular separation between the violet edge (400 nm) and the red edge (700 nm) of the first order spectrum produced by the grating?

Explanation / Answer

a) The basic equation for the n-th order bright line is:

d*sin(angle) = n*wavelength

where d = e-3/430 = (10/6)e-6 = 1.667e-6 (m
=2325 nm

Therefore the order possible is
n =< 2325/[wavelength/(nm)] since sin(angle) =< 1

Since red is the longest wavelength under consideration,
n =< 2325/700 = 3.32

So the highest order is n = 3.

b) Using the same equation in the reverse:
sin(angle) = n * wavelength / d
= 1 * wavelength/(nm) / 2325
angle = Arcsin(wavelength/(nm)/2325)

for wavelength = 700 nm, angle = 17.522 deg
for wavelength = 400 nm, angle = 9.9066 deg

So the angular separation is =7.615 deg

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