Question

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.

Answer #1

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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