You are given an opaque sheet of metal with a narrow slit in it, of width \(d\) (below). You are also given the following: 1) A digital timer; 2) A meter stick; 3) A metric ruler; 4) A light bulb with power cord 5) A laser pointer ( \(\lambda=630 \mathrm{~nm})\); 6) A prism; 7) A projection screen; 8) A mirror Your mission is to measure \(d\) with the proper pieces of the above equipment. a) Check off the equipment you would use. b) Draw a diagram of the experimental setup. c) Describe how you would perform the experiment. d) What would be the difference in the experiment if the metal had two narrow slits cut into it and you were asked to determine the distance between the slits?

The equipment we would use are: 1) A digital timer; 2) A metric ruler; 3) A light bulb with power cord; 4) A laser pointer (\(\lambda=630 \mathrm{~nm}\)); 5) A projection screen. #b) Diagram of the experimental setup#

Draw a diagram with the following arrangement: 1. Place the metal sheet with the narrow slit on a stable base, with the slit held vertically. 2. Set up the laser pointer at a distance from the metal sheet so that the laser beam is directed towards the slit. 3. Position the projection screen behind the metal sheet, at the same height as the slit, to observe the diffraction pattern. 4. If needed, dim the room lights and turn on the light bulb to make the diffraction pattern more visible. #c) Performing the experiment#

The experiment steps are as follows: 1. Turn on the laser pointer and adjust its position so that the laser beam is directed towards the narrow slit on the metal sheet. 2. Observe the diffraction pattern created on the projection screen as the laser light passes through the slit. Adjust the position of the screen and the slit sheet to get a clear pattern. 3. Measure the distance \(L\) between the metal sheet and the projection screen using the metric ruler. 4. Measure the distance between the center of the central bright fringe and the first dark fringe (\(y_1\)) in the diffraction pattern using the metric ruler. Make sure to measure the distance to the first dark fringe on both sides of the central bright fringe and take the average for increased accuracy. 5. Use the formula for single-slit diffraction: \(\dfrac{\lambda}{d} = \dfrac{y_1}{L}\), where \(\lambda\) is the wavelength of the laser light (630 nm), \(d\) is the width of the slit, \(y_1\) is the measured distance between the central bright fringe and the first dark fringe, and \(L\) is the distance between metal sheet and projection screen. 6. Solve for \(d\) using the measured values of \(y_1\) and \(L\), and the given value of \(\lambda\). #d) Difference in the experiment when the metal has two slits#

If the metal sheet had two narrow slits cut into it, the experiment would involve observing the interference pattern, also known as a double-slit interference pattern, instead of the diffraction pattern observed with a single slit. The main difference in carrying out the experiment would be to determine the distance between the slits using the interference pattern. The formula for double-slit interference is \(\dfrac{\lambda}{D} = \dfrac{y_n}{L}\), where \(D\) is the distance between the slits and \(y_n\) is the distance between adjacent bright fringes in the pattern.