Double+sleep+experiment

Joo Yong Sung Mr. Richardson AP Physics B 5/23/2013 Final Project Purpose: The purpose of this project is to find number of lines in unknown diffraction grating. In order to proceed, I repeat Young’s double slit experiment to two different diffraction gratings; one is the number of lines known, and another one is the number of lines unknown. For the experiment of known diffraction grating, I can get the accuracy of the experiment. After I figured out the accuracy, I can do the experiment on the unknown diffraction grating, get result by using equation x= mㅅL/d, and multiply the accuracy, so I can have more accurate result.

Procedure: Prepare the following materials. - Razors with wavelength λ=680nm - Unknown diffraction grating - Known diffraction Grating - Razor, grating holder (2 plastic Cups) - Ruler (meter stick) and white screen. - Duct tape

Before start the experiment, I cut the bottom of the plastic cup and used it for the grating holder. And I taped razor (λ=680nm) at the bottom of cup so I can hold razor more stable. After that, I set the distance from screen to the known diffraction grating (500/mm) at 0.4m. And then i shine the razor through the grating. As a result there were bright spots and dark spots. Distance between the first bright spot and maximum bright spot (x) was 0.1415m. And i plugged length and distance and wavelength in an equation( x= mㅅL/d ), and I got 1.922*10^-6..

Since th e re is 5000 lines in a known fraction grating, there is 5000000 lines in a meter, and each lines are apart for 2e-7m (d). So in order to get accuracy, I divided 2e-7m from 1.922*10^-6 and there is approximately 96% accuracy of the experiment. After the experiment of known grating, I did same experiment on unknown with same distance between screen and grating and it had bright spot (x) of 0.385m. As I plug equation for all this data, I got 7.065*10^-7. Since there is 96% accuracy, I multiplied the number to 1/accuracy, and I got 7.36*10^-7m, which is 1358.7lines per mm.

Analysis: 1) For the experiment of known grating x= mㅅL/d, L= 0.4m, m=1, x= 0.1415m, ㅅ= 680*10^-9m d = ㅅL/x= (680*10^-9) (0.4) / (0.1415) = 1.922*10^-6  Actual d= 1/500000 = 2*10^-6  Accuracy= Actual d/ d = 1.922/2.0 = 0.96 = 96% 2) For the experiment of unknown grating x= mㅅL/d L= 0.4m, m=1, x= 0.385m, ㅅ= 680*10^-9m d= ㅅL/x = (680*10^-9) (0.4) / (0.385)= 7.065*10^-7 Actual d= (1/Accuracy) * d = (1/0.96) * 7.065*10^-7 = 7.36* 10^-7 m Lines in mm= 1/7.36* 10^-4 mm = 1358.7

Result: The result of the calculation seems pretty explanatory. The distance between bright spots in unknown diffraction grating is larger than the known one, and it has more lines than the known one also. Therefore there is inverse relationship with the distance between bright spots and distance between each lines. The previous comment is true because according to the equation x= mㅅL/d, there is inverse relationship with x and d. So the experiment is success.