Light from a lamp, which emits light a several discreet different wavelengths, i

Question

Light from a lamp, which emits light a several discreet different wavelengths, illuminates an 800 line/mm diffraction grating. A screen is placed 50.0 cm behind the grating where the light is observed. Light of wavelength 501.5 nm creates a first-order bright fringe 21.90 cm from the central maximum. (a) What is the wavelength of the first-order bright fringe that is 37.80 cm from the central maximum? (b) If the screen is very long, what is the maximum number of bright fringes for the light of wavelength 501.5 nm?

Explanation / Answer

(a)

slit width a = 1mm/800 = 10^-3/800 = 1.25*10^-6 m

in diffraction

a*y/R = m/2*lambda

y = distance of first order bright fringe

R = distance of screen = 0.5 m

for first bright fringe m = 1

1.25*10^-6*0.378/0.5 = (1/2)*lambda

lambda = 1.89*10^-6 m

++++

b)

a*sintheta = m/2*lambda

1.25*10^-6*1 = m/2*501.5*10^-9

m = 4

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