Question

Coherent light of wavelength 670 nm passes through two parallel slits separated by 0.25 mm. The interference pattern is observed on a screen 90 cm from the slits. If the width of each slit is 0.08 mm, (a) what is the order of the first bright fringe missing from the pattern? (b)how far from the cbf is this missing fringe?

Answer 1

In a double slit experiment, interference and diffraction act together and form a pattern at different positions. An interference of a missing order is formed when the minima of diffraction coincides with the Maxima of the interference.

Now, for the first single slit interference, sin$\Theta$ = n$\lambda$/d where d= width of each slit.

And for the double slit interference, Maxima occurs at

Sin$\phi$ = m$\lambda$/r where, r= distance between the slits.

Therefore to find the missing fringe

For part b, the height of a nth order bright fringe is given by y=n lambdaxD/d, D= distance between the slit and screen,

d= distance between slits