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