A single-slit diffraction pattern is formed when light of wavelength A = 550 nm

Question

A single-slit diffraction pattern is formed when light of wavelength A = 550 nm is passed through a narrow slit. When the pattern is viewed on a screen 0.75 meter away, the width of the central maximum is 0.50 cm. a) What is in meters the width of the slit? b) What is in centimeters the width of the first order fringe (the one next to the central fringe) c) What is in degrees the angular position of the 3rd order minimum? d) How would the pattern change if we use light of higher frequency? the fringes become narrower the fringes become wider frequency does not affect the pattern e) What is in nanometers the wavelength of the second light source if the width of the central maximum in the new pattern is 0.45 cm?

Explanation / Answer

Part A)

Apply y/L = m(wavelength)/a

.01/.95 = 1(490 X 10-9)/a

a = 4.66 X 10-5 m

Part B)

y/.95 = (490 X 10-9)/(4.66 X 10-5)

y = .01 m

Part C)

sin(angle) = 3(490 X 10-9)/(4.66 X 10-5)

angle = 1.81o

Part D)

Higher frequency means smaller wavelength. At a smaller wavelength, the fringes become narrower

Part E)

8.9 X 10-3/(.95) = 1(wavelength)/(4.66 X 10-5)

wavelength = 436.1 nm

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