RYERSON UNIVERSITY DEPARTMENT OF PHYSICS LAB REPORT FOR

PCS 213 SECTION 4/ ( Fill you section here)

TITLE OF EXPERIMENT: DIFFRACTION AND INTERFERENCE OF LIGHT

EXPERIMENTERS: Shivang Patel (500376688)Kody Baum ( )

AUTHORS OF THIS REPORT: Shivang Patel (500376688) [fake my sign here] Kody Baum ( ) [sign here]

EXPERIMENT PERFORMED ON: 6 Feb 2012

REPORT SUBMITTED ON: 13 Feb 2012

TA’S NAME: David Dalla Rosa

Objectives

The purpose of this experiment was to measure the wavelength produced by a monochromatic light source [sodium lamp], as well as to measure the Rydberg constant for hydrogen light bulb. [1]

Background

An American astronomer, David Rittenhouse, made the first diffraction grating in 1785, and reported constructing a half-inch wide grating with fifty-three apertures. A diffraction grating is a collection of reflecting elements separated by a distance comparable to the wavelength of light under study. It may be thought of as a collection of diffracting elements, such as a pattern of transparent slits in an opaque screen. For a diffraction to occur the light source(s) must be in a constant phase. Furthermore, constructive interference will occur only for certain discrete angles of the transmitted rays. [2] [3]

The diffraction angles, θ, at which constructive interference occurs can be found from the equation: dsinθ=nλ eq. 1 [1]

Rydberg constant describes the wavelengths or frequencies of light in various series of related spectral lines, such as those emitted by hydrogen atoms. The value of this constant is based on the premise that the nucleus of the atom emitting light is exceedingly massive compared with a single orbiting electron. [4]

The literature value of the Rydberg constant R∞ is 1.097373157 × 107 per meter.

In this experiment, the Rydberg constant for hydrogen will be found using the equation known as Balmer’s expression.

1λ=R( 122− 1k2 ) eq. 2 [1]

Apparatus

Part A

FIGURE 1 [1]

Part C

FIGURE 2

L

Meter stick

Hydrogen light bulbDiffraction

Grating

Procedure

Part A

1) The sodium lamp was lit and allowed to warm up for about 10 minutes.2) A meter stick was then mounted in front of the sodium lamp just below it.3) The diffraction grating stand was then positioned 0.75 meters away from the

meter stick.4) The diffraction grating was the positioned so that images of the slit were visible

along the meter stick.5) The exact distance between the meter stick and diffraction grating was then

measured.6) The positions of the first two images of the slit on each side of the central image

were then recorded along with the position of the central image.

Part C

1) The room lights were turned off to improve the results of the experiment.2) The meter stick was first set up horizontally and slightly elevated in front of the

hydrogen discharge tube.3) The diffraction grating was then positioned 0.75 meters away from the meter

stick.4) The diffraction grating was the positioned so that spectrum lines were visible

along the meter stick.5) The positions of the first two images of the slit on each side of the central image

were then recorded along with the position of the central image.

Observationsn N d(mm) y(cm) x(cm) ϴ=tan-1(y/x)

(⁰)Sinϴ λ (nm)

1(Left) 100 1/100 60-55.5=4.5

75 3.43 0.0598 598

2(Left) 100 1/100 60-50.9=9.1

75 6.92 0.1204 602

1(Right) 100 1/100 64.4-60= 4.4

75 3.36 0.0586 586

2(Right) 100 1/100 69.1-60= 9.1

75 6.92 0.1204 602

Red (Left) 100 1/100 60-55= 5 75 3.81 0.0664 664Red(Right) 100 1/100 64.7-60=

4.775 3.58 0.0624 624

Blue-Green(Left)

100 1/100 60-56.5=3.5

75 2.67 0.0466 466

Blue-Green(Right)

100 1/100 63.5-60= 3.5

75 2.67 0.0466 466

Violet(Left) 100 1/100 60-56.3= 3.7

75 2.82 0.0491 491

Violet(Right) 100 1/100 63.4-60= 3.4

75 2.59 0.0452 452

TABLE 1Actual value of λ sodium= 589.3nm

Calculations and Results

Sodium Lamp:ϴ=tan-1(y/x) = tan-1(0.045/0.75)=3.43⁰ ↖ϴ=tan-1(y/x)= tan-1(0.091/0.75)= 6.92⁰ ↖ϴ=tan-1(y/x)= tan-1(0.044/0.75)= 3.36⁰ ↗ϴ=tan-1(y/x)= tan-1(0.091/0.75)= 6.92⁰ ↗

Sinϴ= Sin(3.43⁰) =0.0598Sinϴ= Sin(6.92⁰) =0.1204Sinϴ= Sin(3.36⁰) =0.0586Sinϴ= Sin(6.92⁰) =0.1204

λ= dsinϴ/n = (0.00001x0.0598)/1 = 598nmλ= dsinϴ/n = (0.00001x0.1204)/2 = 602nmλ= dsinϴ/n = (0.00001x0.0586)/1 = 586nmλ= dsinϴ/n = (0.00001x0.1204)/2 = 602nmλavg= 597nm

percentage error = (estimate - actual) / actual * 100 = ((597-589.3)/589.3) x 100= 1.31 %

Hydrogen Lamp: Red:

ϴ=tan-1(y/x)= tan-1(0.05/0.75)= 3.81⁰ ↖ϴ=tan-1(y/x)= tan-1(0.047/0.75)= 3.58⁰ ↗

Sinϴ= Sin(3.81⁰) =0.0664Sinϴ= Sin(3.58⁰) =0.0624

λ= dsinϴ/n = (0.00001x0.0664)/1 = 664nmλ= dsinϴ/n = (0.00001x0.0624)/1 = 624nm

Blue-Green:ϴ=tan-1(y/x)= tan-1(0.035/0.75)= 2.67⁰ ↖ϴ=tan-1(y/x)= tan-1(0.035/0.75)= 2.67⁰ ↗

Sinϴ= Sin(2.67⁰) =0.0466Sinϴ= Sin(2.67⁰) =0.0466

λ= dsinϴ/n = (0.00001x0.0664)/1 = 466nmλ= dsinϴ/n = (0.00001x0.0624)/1 = 466nm

Violet:

ϴ=tan-1(y/x)= tan-1(0.037/0.75)= 2.82⁰ ↖ϴ=tan-1(y/x)= tan-1(0.034/0.75)= 2.59⁰ ↗

Sinϴ= Sin(2.82⁰) =0.0491Sinϴ= Sin(2.59⁰) =0.0452

λ= dsinϴ/n = (0.00001x0.0491)/1 = 491nmλ= dsinϴ/n = (0.00001x0.0452)/1 = 452nm

Average experimental wavelength for Red, blue-green and violet respectively:

Red = 644 nm Blue-Green = 466 nm

violet = 471 nm

Using Balmer's equation to find the Rydberg constant for red, blue-green, and violet:

1λ=R( 122− 1k2 )

For the wavelength with the colour red:

1

6.44 (10 )−7m=R( 122− 132 )

R=11,180,124

For the wavelength with the colour blue-green:

1

4.66 (10 )−7m=R( 122− 142 )

R=11,444,921

For the wavelength with the colour violet:1

4.71 (10 )−7m=R ( 122− 1

52 )R=10,110,201

Uncertainty within the experiment: Measuring uncertainty (±0.005m)

Error calculated for Rydberg constant for blue-green because that was the largest uncertainty in the entire procedure.

¿ accepted−experimentalaccepted

∨(100% )=error

error=¿ 10973731.6−1144492110973731.6

∨(100% )

error=4.29%

Discussion of Results and Conclusions

The condition for maximum intensity is the same as that for a double slit, experiment 1. However, angular separation of the maxima is generally much greater because the slit spacing is so small for a diffraction grating.

The diffraction grating is an immensely useful tool for the separation of the spectral lines associated with atomic transitions. It acts as a prism, separating the different colors of light much more than the dispersion effect in a prism.

The hydrogen gas in a thin glass tube is excited by an electrical discharge and the spectrum can be viewed through the grating.

The tracks of a compact disc act as a diffraction grating, producing a separation of the colors of white light. The nominal track separation on a CD is 1.6 micrometers, corresponding to about 625 tracks per millimeter. This is in the range of ordinary laboratory diffraction gratings.

For this particular experiment the average experimental wavelength for Red, blue-green and violet respectively:

Red = 644 nm Blue-Green = 466 nm violet = 471 nm

Using Balmer's equation to find the Rydberg constant for red,

R=11,180,124 ,

for blue-green,

R=11,444,921 and

for violet,

R=10,110,201

The actual Rydberg constant is 1.097373157 × 107 per meter. However, for this experiment the % error calculated for Rydberg constant is 4.29% for blue-green as that color has the largest uncertainty in the entire procedure.

To insure the quality of the experiment the lights were turned off, however, the reasoning for the % error could be the way we were taking the readings as all of readings were close estimation of the real values on the meter stick.

In conclusion, both the equations eq.1 and eq. 2 were verified through this experiment.

Referenceshttp://www.physics.ryerson.ca/sites/default/files/u3/2011/06/DiffractionandInterferenceofLight.pdf [1]

http://physics-animations.com/Physics/English/DG10/DG.htm [2]

http://optics.sgu.ru/~ulianov/Students/Books/Applied_Optics/E.%20Loewen%20Diffraction%20Grating%20Handbook%20(2005).pdf [3]

http://scienceworld.wolfram.com/physics/RydbergConstant.html [4]