A diffraction grating contains 15,000 lines/inch. We pass a laser beam through t

Question

A diffraction grating contains 15,000 lines/inch. We pass a laser beam through the grating. The wavelength of the laser is 633 nm. On a screen 2.55 m away, we observe spots of light. (a) How far (m) from the central maximum (m = 0) is the rst-order maximum (m = 1) observed? (b) How far (m) from the central maximum (m = 0) is the second-order maximum (m = 2) observed? DO NOT use the small-angle approximation," ybright = (?L=d)m. The angles are too large for sin ? ? tan ? to be a good approximation.

Explanation / Answer

d = 1 in/15000 = 1.69E-6 m

a) m lambda = d sin theta

theta = arcsin(1*633.0E-9/1.69E-6)

y = L tan theta = 2.55*tan(arcsin(1*633.0E-9/1.69E-6))=1.03 m

b) 2.55*tan(arcsin(2*633.0E-9/1.69E-6))=2.88 m

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