A slit of width 0.56 mm is illuminated with light of wavelength 502 nm, and a sc

Question

A slit of width 0.56 mm is illuminated with light of wavelength 502 nm, and a screen is placed 110 cm in front of the slit. Find the widths of the first and second maxima on each side of the central maximum.

A slit of width 0.56 mm is illuminated with light of wavelength 502 nm, and a screen is placed 110 cm in front of the slit. Find the widths of the first and second maxima on each side of the central maximum 120.44-5 x Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. mm (1st maxima) = 220.88e-2 × Your response differs from the correct answer by more than 100%. mm (2nd maxima) = 1204465 w1= 120.44e-5 W2

Explanation / Answer

For single slit diffraction, the condition to have a minimum is

a*sin(q) = m*L

where a is the slit width, q is the diffraction angle, m is the diffraction order, and L is the wavelength. For small diffraction angles, this may be approximated as

a*y/D = m*L

where y is the distance from the central peak to the minimum of order m, and D is the distance from the slit to the screen.

Solving for the displacement of the minimum

y = m*L*D/a

for first maxima, m =1

y = 9.86e-4 m

for second maxima, m=2

y = 1.97e-3 m

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