Q4DQ - University Physics with Modern Physics

Question

In a two-slit interference pattern on a distant screen, are the bright fringes midway between the dark fringes? Is this ever a good approximation?

Step-by-Step Solution

Answer

For the bright fringe’s midway between the dark fringes, if the angle of diffraction $\mathit{\theta }$ is sufficiently small then the approximation is good.

Step 1: Define the principle of superposition

The principle of superposition states: 

When two or more waves overlap, the resultant displacement at any point and at any instant is found by adding the instantaneous displacements that would be produced at the point by the individual waves if each were present alone.

Step 2: Determine whether the approximation is good or not.

To have bright fringes midway between the dark fringes:

For bright fringes the relation is $\mathrm{d} {\mathrm{sin\theta }}_{\mathrm{m}}=\mathrm{m\lambda }$

And for dark fringes relation is $\mathrm{d} {\mathrm{sin\theta }}_{\mathrm{m}}=(\mathrm{m}+\frac{1}{2})\mathrm{\lambda }$

Thus, for good approximation $\theta$ needs to be sufficiently small.