Question

A double slit is opposite the center of a 1.8 -m-wide screen that is \(2.0 \mathrm{~m}\) away. The slit separation is \(24 \mu \mathrm{m},\) and the width of each slit is \(7.2 \mu \mathrm{m} .\) How many bright fringes are visible on the screen, including the central maximum, if the slit is illuminated by \(600 .-\mathrm{nm}\) light?

Short answer

Answer: There are 17 bright fringes visible on the screen, including the central maximum.

Step-by-step solution

Calculate the maximum fringe order m

We need to find the maximum value of \(m\) such that \(y_m ≤ \frac{W}{2}\). Using the double-slit interference formula, \(y_m = L\frac{mλ}{d}\): \(\frac{W}{2} = L\frac{mλ}{d}\) Now, solve for \(m\): \(m = \frac{Wd}{2Lλ}\)

Input the given values and calculate m

Input the given values: \(m = \frac{(1.8 \mathrm{~m})(24 \times 10^{-6} \mathrm{~m})}{(2)(2.0 \mathrm{~m})(600 \times 10^{-9} \mathrm{~m})}\) \(m \approx 9\) So, there are 9 bright fringes on the top half of the screen. However, we need to consider both the top and bottom halves of the screen to find the total number of bright fringes.

Calculate the total number of bright fringes

Since there are 9 bright fringes on the top half of the screen and we have symmetry about the central maximum: Total number of bright fringes = (2 × 9) - 1 = 17 (Subtracted 1 because the central maximum is counted twice) We find that there are 17 bright fringes visible on the screen, including the central maximum.