Question

# Light with a wavelength of 702 nm passes through a slit 7.50 ?m wide and falls...

Light with a wavelength of 702 nm passes through a slit 7.50 ?m wide and falls on a screen 2.05 m away. Find the linear distance on the screen from the central bright fringe to the first bright fringe above it. Express your answer to three significant figures.

given

wavelength of light, lambda = 702*10-9 m

slit width, d = 7.5*10-6 m

distance from the slit to the screen, L = 2.05 m

and we have the formula for path difference of brightness in case of single slit diffraction as

d sin(theta) = (2m+1)*lambda/2

for first bright fringe, m =1

therefore, d sin(theta) = 3*lambda/2

theta = sin-1[3*lambda/2d]

theta = sin-1[3*702*10-9/2*7.5*10-6]

so, theta = 8.07 o

now the linear distance (x) on the screen from the central bright fringe to the first bright fringe above it is

tan (theta) = x /L

or   x = L tan (theta)

x = 2.05*tan 8.07 o

linear distance, x = 0.291 m

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