Question

Below is an image from a double slit experiment obtained by shining a laser through one. I used a He-Ne Laser, wavelength = 632.8 nm, and shined through two slits whose separation distance is d = 0.250 mm. The light was shined upon a sheet of paper taped to the wall and was 10.0 ft 4.00 inches away from the double slit. I circled the bright spots (constructive interference) and identified the central maximum (m = 0). I saved the lab data as a pdf file with a 1:1 ratio. I was able to identify seven bright fringes on either side of the central maximum. Let ym measure the distance from the central maximum to the mth constructive interference. For positive m, let ym be positive, and for negative order (negative m), let ym be negative. The geometry of the double slit experiment is shown below ym, m o d m=0 L For constructive interference, the path difference between the two waves that pass through the slits must be an integer multiple of the light's wavelength. For the mth order of constructive interference, we have path difference 8 = d sin 0 = md. Since L >> d, we can use the small angle approximation that the sine of the angle is approximately equal to the tangent of the angle. Consequently, we can rewrite the equation as d sin ~ d tan = d Ут L = m2 We will use the provided data to determine the experimental value of the wavelength of the laser used. To accomplish this, we will measure the distance ym from the middle of the center (m = 0) maximum to the middle of the mth constructive interference maximum and record this measurement. Remember for positive m, the value ym is positive and for negative m, the value of ym is negative. Once this is completed, instead of solving for each value of the wavelength, we will create a scatter plot in a manner similar to the one used in the Snell's Law experiment. Take the derived equation and solve for the wavelength. d.Ym = ma You should get dym rise 2= ml run

ive attached the results to the experiment help me how to find ym in oder to get the y values to plot the data and get the slope

Answer 1

Given. Id-dym ML şo > AmL d form=1 -9 Yo = 632.8x16X1X3.048 0.250X 163 Im = d=632.8x10 m d=0.250 X 103 m L= 10ft = 3.048m m Ym = dml व 1 0.0077 0.0154 3 0.0231 4 0.0308 S 0.0385 6 0.0462 7. 0.0539 Ym = 0.0077m g

for the % enor you have to calculate Experimentel value of nexp. then apply formula the % Enarinda nexpo Ath -x 100. Ati Wohere ath=632.8.mm curve ro ie → for nexp you have to plate between dym="y" & ML = "X" anis & find the slop. a= dym me dym = a 'dmi a 'dme compare with straight line agr "Ymx'te dyon Here Slop = m = 4/C=0 "Y Exp me Here (dyn Adym There Adym Дm L KAML " (ML)