Experiment 12 - wavelength of light PDF

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wavelength of light...

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4/29/2021 Experiment 12

Purpose/Goal: The purpose of this experiment is to determine the wavelength of light emitted by a LASER using both light interference and diffraction grating. We will learn how to create a light interference pattern on a screen using a LASER that shines through a double slit. We will then determine the distance between the constructive maxima that appear on the light interference pattern from the double slit. Next, we will determine the wavelength of light from the LASER using the distance found in the previous step. It will then be important to use diffraction grating to create a light diffraction pattern by using the LASER, and later determine the distance between constructive maxima in a diffraction pattern which will allow us to find the wavelength of light from the LASER. Procedure: Part A: 1) Notice the picture shown in part A of the lab guide and include it in your lab report. 2) Record the values of d, n, the central maximum, and the last bright spot in the lab report. 3) Divide the total distance between the first and last maximum by 10 to determine the spacing (∆y) between each bright spot. 4) Assuming that the values for d have an error of 2%, determine the value of d with most probable error. 5) The distance between the double slits and the screen (L) was found to be 1,655 mm; convert this value to meters and record it in the lab report. 6) Use Min/Max and Equation 6 to determine the wavelength of the light emitted by the LASER with error. 7) Repeat Steps 1-6 using a second set of double slits. 8) Find the percent error of the wavelengths found using double slits A and B compared to the actual wavelength of the LASER (633 mm). Part B: 1) Use the values of the central maximum and the position of the last bright spot to help calculate the value of y; record all values in the lab report. 2) Use Equation 3 and the value of L to determine the value of α for this optical system. 3) Assuming that the values for d have an error of 2%, determine the value of d with most probable error 4) Use Max/Min, the value of d, and the value of α to calculate the wavelength of the light emitted by the LASER with error. 5) Find the percent error of the measured wavelength to the actual wavelength of the LASER (633 mm). 6) Discuss which method, between the double slit method and the diffraction grating method, is more accurate for determining the wavelength of the LASER and why. Data, Part A:

Figure 1: Light interference pattern produced by the LASER and the double slit.

Double Slits A: distance between slits: 0.25 mm # of bright spots: 11 position of central maximum: 23 mm position of last bright spot: 65 mm distance between double slits & screen (L): 1,655 mm = 1.655 m Double Slits B: distance between slits: 0.50 mm # of bright spots: 21 position of central maximum: 28.5 mm position of last bright spot: 70 mm distance between double slits & screen (L): 1.655 m

Calculations, Part A: Double Slits A: total distance between first and last bright spot: 65 mm - 23 mm = 42 mm spacing (∆y) between each bright spot: ∆y = 42 / (11-1) = 4.2 mm = 0.0042 m “d” with error: 0.25*0.02 = 0.0336 mm d = (0.25 ± 0.034) mm =

(0.00025 ±3.4 x 1 0−5 )m

Min/Max vwavelength of the light: ∆y = (L/d) λ λ = ∆y(d/L)

λ avg=∆ y (d avg / L) λ avg=( 0.0042)(0.00025 /1.655)

λ avg=6.34 x 1 0−7 m λmin = ∆y( d min /L) λmin = (0.0042 )[(0.00025−3.4 x 1 0−5 )/ 1.655] λmin = 5.48 x 1 0−7 m d max / L ) λmax =∆ y ¿ −5

λmax =(0.0042) [( 0.00025 +3.4 x 1 0 )/ 1.655 ] −7

λmax =7 .21 x 1 0 m

λerror =( λmax −λ min )/ 2 −7

−7

λerror =(7.21 x 10 −5.48 x 1 0 )/ 2 λerror =8.65 x 1 0−8 m λ=(6.34 x 1 0−7 ±8.7 x 10−8 )m λ = (634 ± 87) nm Double Slits B: total distance between first and last bright spot: 70 mm - 28.5 mm = 41.5 mm spacing (∆y) between each bright spot: ∆y = 41.5 / (21-1) = 2.075 mm = 0.002075 m “d” with error: 0.5*0.02 = 0.01 mm d = (0.5 ± 0.01) mm =

(0.0005 ±1 x 1 0−5 )m

wavelength of the light: ∆y = (L/d) λ λ = ∆y(d/L)

λ avg=∆ y (d avg / L) λ avg=( 0.002075)( 0.0005 / 1.655) λ avg=6.27 x 1 0−7 m λmin = ∆y( d min /L) λmin = (0.002075 )[(0.0005 −1 x 10−5)/ 1.655 ]

λmin = 6.14 x 1 0−7 m d max / L ) λmax =∆ y ¿ λmax =(0.002075 )[(0.0005+1 x 1 0−5 )/1.655] λmax =6.39 x 1 0−7 m λerror =( λmax −λ min )/ 2 −7

−7

λerror =(6.39 x 1 0 −6.14 x 1 0 )/2 λerror =2.5 x 1 0

−8

m

λ=(6.34 x 1 0−7 ±2.5 x 1 0−8)m λ = (634 ± 25) nm

Percent Error of Double Slit A/B Wavelength with Actual Value: (calculated wavelengths of Double Slits A/B were identical) % error: |observed-actual|/actual % error: |634-633|/633 % error: 0.16%

Data, Part B: position of central maximum: 175 mm position of last bright spot: 650 mm distance from diffraction grating to screen (L): 1,140 mm = 1.14 m Calculations, Part B: value of y: 650 - 175 = 475 mm = 0.475 m

α: tan (α)= y /L tan (a)=0.475 /1.14 α = arctan(0.4166667) α = 22.6°

value of

“d” with error:

1.667 x 1 0−6 m 1.667 x 1 0−6 (0.02) = 3.334 x 1 0−8 m d = (1.667 x 1 0−6 ± 3.334 x 1 0−8 )m d=

λ with error: λ=dsinα

value of

λ avg=d avg sinα −6

λ avg=(1.667 x 10 )sin 22.6 ° λ avg=6.38 x 1 0−7 m λmin =d min sinα λmin =(1.667 x 1 0−6 −3.334 x 1 0−8 )sin 22.6 ° λmin =6.29 x 1 0−7 m λmax =d max sinα λmax =(1.667 x 1 0−6 +3.334 x 10−8)sin 22.6 ° λmax =6.53 x 1 0−7 m λerror =( λm ax− λmin )/2 −7

−7

λerror =(6.53 x 1 0 −6.29 x 10 )/2 8

λerror =1.2 x 1 0 m

λ=(6.38 x 1 0−7 ± 1.2 x 1 0−8 )m λ=(638 ± 12)nm Percent Error with Actual Wavelength Value: % error: |observed-actual|/actual % error: |638-633|/633 % error: 0.7% Questions: 6) It looks the double slit interference patterns (specifically, double slits B) will be more accurate in determining the wavelength for the light emitted by the LASER. The average values for the wavelength for both double slits A and B were closer to the true wavelength of the LASER than the value found using the diffraction grating. I would argue that double slits B is the more accurate out of both double slits because although they obtained the same average wavelength,

double slits B had a lower error value and thus the value of the wavelength with error was confined to values closer to the average value. Conclusion: The experimental values found using double slits A, double slits B, and the diffraction grating were 634 nm, 634 nm, and 638 nm. The percent errors for the double slits compared to the actual value of the wavelength of the LASER were 0.16%, whereas the percent error for the diffraction grating compared to the actual value of the wavelength of the LASER was 0.7%. Based upon the significantly low values of the percent errors between the observed and actual values of the wavelength, I would claim that this experiment was conducted successfully and that all objectives were met. Error Analysis: Although there was very little error found in this experiment, some error may have been introduced during the measurements of the bright spots. Because the brightness of the maxima fades along the sides, it would be harder to see the last bright spots. It would be hard to measure something that isn’t easy to see, which would inevitably introduce errors when calculating the total distance between the 1st and last bright spot, and also when determining the spacing (∆y) between each bright spot....