Question

(Diffraction and Interference of Light)

We think of the width of the central maxima on a screen as a measure of the uncertainty in the direction of travel of the photons. What happens to this uncertainty in the direction of travel (momentum) as the slit width narrows? Defend your answer using equations

Answer 1

From Heisenberg's Uncertainty Principle

del (X) * del ( p) >= h / 4 pie                 

Here x = position of particle, del x = uncertainty in position of particle

del p = uncertainty in momentum,                    h = planck constant

If we decrease the distance between slits ie we are decreasing del (X).

Then according to uncertainty principle, when del (X) is decreasing, then del (p) will increase to maintain this inequality.

more we are going to decrease the distance between slits ie.[ ( del x ) decreases], uncertainty in momentum (del p) will increase.

This increase in uncertainty in momentum will provide greater spreading of photon, which provide wider spot on screen.