Example 14.1: Double slit experiment

Question: Coherent light of wavelength $633\,{\rm nm}$ from a He-Ne laser falls on a double slit with a slit separation of $0.103\,{\rm mm}$. An interference pattern is produced on a screen $2.56\,{\rm m}$ from the slits. Calculate the separation on the screen of the two fourth-order bright fringes on either side of the central image.
 
Solution: The easiest way to handle this problem is to calculate the distance $y_4$ of the fourth-order bright fringe on one side from the central image, and then double this value to obtain the distance between the two fourth-order images. From Eq. (375),

$$y_4 = \frac{4\,\lambda\,L}{d} =\frac{4\,(633\times 10^{-9})\,(2.65)}{(0.103\times 10^{-3})} = 6.29\,{\rm cm}.$$

The distance between the two fourth-order fringes is therefore

$$2\,y_4 = 12.6\,{\rm cm}.$$