(a) For a grating, how many lines per mm would be required so that the first ord

Question

(a) For a grating, how many lines per mm would be required so that the first order diffraction line for 500nm is observed at a reflection angle of 10 degrees when the angle of incidence is 60 degrees? (b) What wavelength would be observed at a reflection angle of 50 degrees? (c) if the number of lines/mm is decreased by a factor of 4, what wavelengths would be observed with the angle of incidence of 60, reflection angles of 10 and 50 degrees? (d) How does the span of wavelength compare to that with the "higher precision" grating?

Explanation / Answer

a) n = d(sin i + sin r)

d = n/(sin i + sin r) = (1*500nm)/(sin10 + sin 60) = 480.9 nm

Lines/mm = (1 line/480.9 nm)*(10^6 nm/1 mm) = 2079.4 lines/mm

b)   = d(sin i + sin r) = 480.9*(sin60 + sin50) = 784.86 nm

c) if the number of lines/mm is decreased by a factor of 4 ====> Then d spacing will increase by factor 4 ====> Wavelength will increase by factor 4

So for r = 10 degree =======> = 2000 nm

and for r = 50 degree ======> = 3139.44 nm

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