Q9DQ - University Physics with Modern Physics

Question

 Coherent light with wavelength $\mathit{\lambda }$ falls on two narrow slits separated by a distance $\mathit{d}$. If $\mathit{d}$ is less than some minimum value, no dark fringes are observed. Explain. In terms of $\mathit{\lambda }$, what is this minimum value of $\mathit{d}$?

Step-by-Step Solution

Answer

In terms of $\lambda$, if $d<<\lambda$, then no interference will take place.

Step 1: Define the principle of superposition.

The principle of superposition states: 

For a particular wavelength and constant distance between slits and screen, the fringe width is inversely proportional to the distance between two slits. Thus smaller the separation, the larger the fringe width.

Step 2: Determine if &#955; &#62; &#62; d whether there is interference or not.

When $\mathrm{d}<<\mathrm{\lambda }$, the waves of light will become almost parallel and will have the same phase at each point. That will create a single slit situation.

Hence, if $\mathrm{d}<<\mathrm{\lambda }$, then there is no interference.