Chapter 11.3, Problem 2aT

Consider a point M on the distant screen where there is a maximum due to the light from $S_1\text{and}{S}_2$ .

If a third slit were added as shown at right, would there still be maximum constructive interference at point M? Explain.

Suppose that more identical slits were added with till adjacent slits a distance d apart.

Would there still be maximum constructive interference at point M? Explain.

Let $\Delta D_{\text{adj}}$ represent the difference in distances from two adjacent sub to a location on the screen. For two slits, you found that any point of maximum constructive interference is farther from one of the slits by a whole number of wavelength (i.e., $\Delta D\text{is}0,\lambda ,2\lambda ,\mathrm{...}$ ).

For three or more evenly-spaced slits, what is the corresponding condition for locations of maximum constructive interference? Express this condition in terms of $\Delta D_{\text{adj}}$ .

We will call a location at which light from all of the slits is in phase a principal maximum.