2:31 54 Search Diffraction.pdf We will study the interference of light in today's lab. Open the simulation: 3 of 7 com/15.html ;lit distance d equal to 3um. The wavelength of the light by default is 400 nm so ...t/blue color light. Change the wavelength of the light to 550 nm. You will notice the light turn green. Step 2: Click on the button "Show Interference Pattern". Now you will see the interference pattern on the screen placed at a distance of 10um from the double slits. Notice that the light waves coming from the two slits are in phase when they arrive at the bright spots and are completely out of phase when they arrive at the dark spots. Step 3: Calculate the angle for the first order maxima (m = 1) using the equation below for the double slit experiment. d sin 0= ma Remember that: d = 3um = 3 x 106 m 2 = 550 nm = 550 x 10" m Show all your work below to find the angle 0, for m = 1. 01 (theory) = Step 4: Calculate the angle for the second order maxima (m = 2) now, for the same d and a that you used in Step 3 above. Show all your work below. 02 (theory) = Step 5: Go back to the simulation now, and check the "Show Scale" box and uncheck the "Show Wavefronts" box. On the screen measure the distance y , from the central bright spot (where 0 is) to the first order maxima. y1 = The distance to the screen Is. L - Topmm2:31 54 Search Diffraction.pdf 02 (theory) = 4 of 7 Step 5: Go back to the simulation now, and check the "Show Scale" box and uncheck the "Show Wavefronts" box. On the screen measure the distance y , from the central bright spot (where 0 is) to the first order maxima. y1 = The distance to the screen is: L = 10um Find the angle 0, using the equation below. Show all your work. tan 0= L 01 (experiment) = Step 6: Find the percent error. Show all your work below. % error=- 0, theory) -0, (experiment ) x 100 0, (theory) % error= i Step 7: Go back to the simulation now, and measure the distance yz from the central bright spot (where 0 is) to the second order maxima. Y2 = The distance to the screen is still: L = 10um Find the angle 02 using the equation below. Show all your work. tan 0, =12 L 02 (experiment) =2:31 54 Search Diffraction.pdf 2 of 7 originating from the two slits. The length of the path that each wave travels to a particular spot on the screen determines the phase of the wave at that location. Locations where two waves arrive in phase are the brightest; locations where two waves arrive with different phases are darker; and locations where the waves arrive completely out of phase are dark. The geometry for finding the position of the mth bright band on a screen. mth Pm m x bright Path length band wave 1 A.... ym Path length -N Oth wave 2 0 * bright d sin 0m = mad -1 band 2 Slits - 2 Screen For bright spots: d sin 0m = ma m = 0, +1,+2,+3, etc. For dark spots: d sin 0m = (m + 1/2) a We will study the interference of light in today's lab. Open the simulation: https://ophysics.com/15.html Step 1: Set the slit distance d equal to 3um. The wavelength of the light by default is 400 nm so you see a violet/blue color light. Change the wavelength of the light to 550 nm. You will notice the light turn green. Step 2: Click on the button "Show Interference Pattern". Now you will see the interference pattern on the screen placed at a distance of 10um from the double slits. Notice that the light waves coming from the two slits are in phase when they arrive at the bright spots and are completely out of phase when they arrive at the dark spots. Step 3: Calculate the angle for the first order maxima (m = 1) using the equation below for the double slit experiment. d sin 0, = ma Remember that: d = 3um = 3 x 106m 2 = 550 nm = 550 x 10" m Show all your work below to find the angle 0, for m = 1.2:31 54 Search Diffraction.pdf Measure the distance y, from the central bright spot (where 0 is) to the first order maxima. 7 of 7 the screen is: L = 10um rinu we angie 0, using the equation below. Show all your work. y1 tan 0 1= T. 01 (experiment) = Step 11: Find the percent error. Show all your work below. % error= 0, (theory) -0, (experiment ) 0, (theory x 100 % error= i2:31 54 Search Diffraction.pdf 6 of 7 Step 10: Go back to the simulation now, set the slit distance d = 2um and 2 = 700 nm. Paste a picture (or screenshot) of the simulation in the space below. Measure the distance y, from the central bright spot (where 0 is) to the first order maxima. y1 = The distance to the screen is: L = 10um Find the angle 0, using the equation below. Show all your work. tan 01= = y1 01 (experiment) = Step 11: Find the percent error. Show all your work below. % error=- 0, theory) -0, (experiment) -x 100 01 (theory2:31 54 Search Diffraction.pdf Diffraction of Light Name: Testing experiment Prediction Outcome We shine a laser beam on a glass plate covered with a We will see two bright regions on the screen The screen displays many equally spaced black film. The film has two very narrow slits that are that are reduced in height compared to the bright regions with varying levels of bright- very close to each other. Light passes through the slits slits due to the narrow laser beam. ness with the brightest point at the center. and reaches a screen that is parallel to the plate. Glass plate covered What pattern with black film will we see? Laser Screen Conclusion The prediction based on the particle model of light does not match the outcome, disproving the particle model. Double-slit wave interference. (a) (b) (c) Bright bands in the screen Slit Bright Oth Dark 0 order 0 maximum Slit 2 Dark A/2 Laser beam The waves travel equal distances and are in The lower wave travels )/2 farther than the phase when they reach the screen upper wave. They are out of phase when they reach the screen. (d) (e) Bright 2nd order maximum (0) .. Waves are Bright Ist in phase. order wwwwwww maximum - -. Intensity The wave from the lower slit travels one wave- The wave from the lower slit travels two wave- The peaks correspond to the maximum length farther than the wave from the upper slit. lengths farther. brightness on the screen, and the troughs At the screen, they are in phase and interfere correspond to dark regions. constructively. The interference pattern of dark and bright bands produced by light passing through two closely spaced narrow slits can be explained by the addition or superposition of circular wavelets originating from the two slits. The length of the path that each wave travels to a particular spot on the screen determines the phase of the wave at that location. Locations where two waves arrive in phase are the brightest; locations where two waves arrive with different phases are darker; and locations where the waves arrive completely out of phase are dark. The geometry for finding the position of the mth bright band on a screen. mth Pmm x bright Path length band wave 1 ym Path length -N Oth d wave 2 * bright d sin 0m = md - 1 band Slits -22:31 54 Search Diffraction.pdf % error= i : to the simulation now, and measure the distance yz from the central bright spot 5 of 7 he second order maxima. The distance to the screen is still: L = 10um Find the angle 02 using the equation below. Show all your work. tan 0, =2 L 02 (experiment) = Step 8: Find the percent error. Show all your work below. 02 theory) -02 (experiment) % error= 02 (theory x 100 % error= i Step 9: Using the equation for the double slit experiment, calculate the first order maxima angle 01 for wavelength 2 = 700 nm (red) and d = 2um assuming L = 10 um. Show all your work below. d sin 0m = ma 01 (theory) = Step 10: Go back to the simulation now, set the slit distance d = 2um and 2 = 700 nm. Paste a picture (or screenshot) of the simulation in the space below