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Nanyang Technological University

School of Physical and Mathematical Sciences

Division of Physics and Applied Physics

PH 1199 Physics Lab Ib

Experiment 4&6: Interference, Diffraction of Light

and Atomic Spectra

Experiment 4: Interference and Diffraction of Light

Background

Diffraction of light occurs as it passes through a slit (Fig. 1). The angles of the minima

in the diffraction pattern are given by

sin = (1)

where is the slit width, is the angle from the centre of the pattern to the m-th minimum,

is the wavelength of the light and = 0, 1, 2, 3, is the order of the superposition.

Figure 1: (a) Single slit diffraction pattern. (b) Double slit interference pattern.

Diffraction of light were first carefully observed and characterized by Francesco Maria

Grimaldi, who also coined the term diffraction, from the Latin; diffringere, to break into

pieces, referring to light breaking up into different directions. The results of Grimaldis

observations were published posthumously in 1665. Isaac Newton studied these effects and

attributed them to inflexion of light rays. James Gregory (16381675) observed the diffraction

patterns caused by a bird feather, which was effectively the first diffraction grating.

(a) (b)

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When light passes through two slits (Fig. 1), the two light rays emerging from the slits

interfere with each other and produce interference fringes. The angles of the maxima in the

interference pattern are given by

sin = (2)

where is the slit separation, is the angle from the centre of the pattern to the m-th maximum,

is the wavelength of the light and = 0, 1, 2, 3, is the interference order. In 1803

Thomas Young did his famous experiment observing interference from two closely spaced slits.

Explaining his results by interference of the waves emanating from the two different slits, he

deduced that light must propagate as waves. Augustin-Jean Fresnel did more definitive studies

and calculations of diffraction, published in 1815 and 1818, and thereby gave great support to

the wave theory of light that had been advanced by Christiaan Huygens and reinvigorated by

Young, against Newtons particle theory.

Apparatus

PASCO Optic bench and screen from the Basic Optics System OS-8515

PASCO Light Sensor CI-6504A

PASCO Rotary Motion Sensor CI-6538

PASCO Aperture bracket OS-8534

PASCO Diode laser OS-8525

PASCO Diode laser OS-8525

PASCO Single slit disk OS-8523

PASCO Multiple slit disk OS-8523

Metric ruler

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Figure 2: Apparatus used for Experiment A.

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Procedures

Part I: Diffraction from a Single Slit

(a) (b)

Figure 3: (a) The experimental setup, and (b) a different view of the experimental setup, showing the optical bench with diode laser and slit.

1. Setup the laser and place the single slit disk in its holder in front of the laser, as shown

in Fig.3.

2. On the single slit disk, select the single slit with = 0.04 .

3. Shine the laser on the centre of the slit.

4. Measure the distances from the slit to the screen, slit to laser and screen to laser.

5. On the Science Workshop 750 Interface, connect the Light Sensor to Analog Channel

A and the Rotary Motion Sensor to Digital Channels 1 and 2.

6. To measure the diffraction pattern shown in Fig. 1(a), move the light detector along the

linear translator.

7. Obtain the graph of light intensity against position using DataStudio.

(Note: Adjust the sample rate and the sensor gain for the best results.)

8. Repeat experiment with = 0.08 and = 0.16 slit widths.

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Part II: Interference from a Double Slit

1. Setup the laser and place the multiple slit disk in its holder in front of the laser.

2. Select the double slit with width = 0.04 and separation = 0.25 .

3. Shine the laser on the centre of the slit.

4. Measure the distance from the slit to the screen, slit to laser and screen to laser.

5. To measure the interference pattern shown in Fig. 4, move the light detector along the

linear translator.

6. Obtain the graph of light intensity against position using DataStudio.

Figure 4: Double slit interference within a single slit diffraction envelope.

7. Measure and record the distance between the first order ( = 1) and second order ( =

2) marks.

8. Repeat experiment with width of = 0.08 and slit separation of = 0.25 ,

followed by = 0.04 and = 0.50 , and finally with = 0.04 and =

0.25 .

*Note: Setting up DataStudio

i. Create new experiment.

ii. Choose system interface in Setup tab.

iii. Assign the sensors to the Analog and Digital Channel.

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Experiment 6: Atomic Spectra

Background

Emission Spectrum

Every atom has a set of discrete energy levels occupied by its electrons. When an electron

makes a transition from a higher energy level to a lower energy level, a photon is emitted. The

wavelength; , of the photon is related to the change in energy of the electron by

=

(3)

where is the Plank constant and the speed of light in vacuum.

As there are many possible transitions between the energy levels in a given atom, photons

of different frequencies will be produced. An atoms emission spectrum is the set of all these

photon frequencies. Since different elements have different atomic structures and different

atomic energy levels, the spectrum will be different for each element. In this way, an emission

spectrum can be used to identify an element.

However, the intensities of each spectral line will depend on the quantum mechanical

probabilities of electrons making transitions between particular states. Therefore, intensities of

spectral lines are hard to calculate. Nevertheless, tables that describe the relative intensities of

the spectral lines for different elements are available in this experiment.

Diffraction Grating

A grating is a piece of transparent material onto a large number of equally-spaced,

parallel lines has been ruled. If diffracted light rays from adjacent lines on the grating

interfere constructively, and image of the light source will be formed. Light rays from

adjacent lines will be in phase if the rays differ in path length by an integral number of

wavelengths of the light. The relationship between the wavelength of light; , the diffraction

line spacing; , and diffraction angle , is;

sin = (4)

As shown in Fig. 6, the path length for Ray A is one wavelength longer than the path length

for Ray B.

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Figure 5: Ray diagram for the first-order diffraction maximum.

Spectrometer

A spectrometer is an instrument for analysing the spectra of radiations. Various forms of the

spectrometer are used to study different parts of the electromagnetic spectrum and for different

purposes. In its simplest form, a spectrometer consists of three basic components: a collimator,

a refracting or diffracting element to separate light into its various components, and a telescope.

Sometimes a diffraction grating is used in place of the prism for studying optical spectra. Figure

6 shows the schematic diagram of a spectrometer.

Figure 6: Schematic diagram of a spectrometer.

The light to be analysed enters the collimator through a narrow slit positioned at the focal

point of the collimator lens. The light leaving the collimator is therefore a thin, parallel beam.

The beam of light passes through the diffracting element placed on a spectrometer table, which

can be rotated, raised and lowered, and levelled. The diffracting element deviates each

component of light by different amounts, producing a spectrum. With the telescope focused at

infinity and positioned at an angle to collect the light of a particular colour, a precise image of

the collimator slit can be seen. By rotating the telescope, the slit images corresponding to each

constituent colour can be viewed and the angle can be measured. These angles can then be used

to determine the wavelengths that are present in the light.

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The glass-prism spectrometer is convenient for measuring ray deviations and refractive

indices, and also for determining unknown wavelengths. However, a glass prism does not

separate the different light as effectively as a grating. For more precise work and also for

recording the relative intensity of each colour of light, we can use a diffraction grating with a

spectrophotometer system with data-logging capabilities.

The light sensor in the system that we will be using makes use of a photodiode that is

responsive across a wide spectrum ranging from 320 to 1100 . By interfacing the light

sensor and a rotary motion sensor with the computer, relative light intensities across a whole

range of angles can be recorded. Since a prism refracts the light into a single spectrum whereas

the grating divides the available light into several spectra, slit images formed using a grating

will be dimmer.

Also, stray light has to be shielded off as much as possible and recording of the spectra

has to be done in the dark.

Apparatus

PASCO SE-9461 Hydrogen Spectral Tube

PASCO SE-9462 Helium Spectral Tube

PASCO SE-9463 Argon Spectral Tube

PASCO SE-9467 Neon Spectral Tube

PASCO OS-9286A Mercury Vapour Light Source

PASCO OS-9287B Low Pressure Sodium Light Source

PASCO OS-8537 Spectrophotometer System

PASCO CI-6538 Rotary Motion Sensor

PASCO CI-6604 High-Sensitivity Light Sensor with Aperture Bracke

PASCO SE-9359 600 line mm-1 Diffraction Grating

PASCO Science Workshop 750 Interface

ELECTRO-TECHNIC PRODUCTS INCORPORATED SP200V Spectral Tube

Power Supply and Mount

(Student Model) Prism Spectrometer

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Figure 7: Apparatus used for Experiment B.

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Procedures

BEWARE! Be extremely careful not to break any emission tubes. One of them contains

mercury vapour. If that tube breaks, inform your instructor immediately.

BEWARE! Be extremely careful not to touch the lamps during/after use. They do reach a

high temperature.

CAUTION!!

Handle the lenses only by their plastic parts.

Avoid touching the grating except by the edges of the glass plate.

Do not touch the spectral tubes in the middle section and do not touch the high

voltage terminals.

Turn on the mercury lamp as soon as you reach the lab before setting up other equipment to

allow it to warm up.

Part I: Viewing the Mercury Spectrum with the Grating Spectrometer

Figure 8: The different parts of a spectrometer.

1. Refer to Fig. 8 on how to set up the experiment and to perform measurements.

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2. To focus the telescope and the collimator:

a) Place the spectrometer on a flat surface and level the spectrometer table by adjusting

the three thumbscrews.

b) While looking through the telescope, pull and push the eyepiece in and out to bring

the cross-hairs into sharp focus. Loosen the graticule lock ring and orientate the

cross-hairs so that one of the cross-hairs is vertical. Retighten the lock ring and

refocus if necessary.

c) Focus the telescope at infinity by focusing on a distant object.

d) Check that the slit plate is slightly open. Loosen the lock screw for telescope rotation

and turn the telescope so that it is directly opposite the collimator.

e) While looking through the telescope, turn the focus knob on the collimator until the

slit comes into sharp focus. DO NOT change the focus of the telescope after this

step.

3. To mount the diffraction grating and viewing the spectra lines

a) Mount the diffraction grating on the spectrometer table as shown in Fig. 8.

b) Place the mercury light source a few centimetres behind the slit.

c) Draw the curtains around the experiment setup to darken the surroundings. Use the

opaque cloth to further shield off stray light around the mercury light source.

d) Turn the telescope and the table until the mercury line spectrum comes into view.

While looking through the telescope, rotate the spectrometer table slightly back and

forth until you observe the spectra lines.

e) Rotate the telescope to align the vertical cross-hair with the fixed edge of the slit

image. Use the fine adjust knobs to make these adjustments as precisely as possible,

then measure the telescope angle using the Vernier scale.

4. Observe the spectral lines of mercury given in Table 1 and record the corresponding

angles to compute the wavelength for the first order = 1.

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Table 1: The Atomic Mercury Emission Spectrum.

Colour Recorded Angle () Wavelength (in ) Visual Intensity

Violet 4046.56 Strong

Blue Very Strong

Turquoise Strong

Green 5460.74 Very Strong

Yellow 5769.59 Strong

Part II: Recording the Hydrogen Spectrum with the Grating Spectrophotometer

(a)

(b)

Figure 9: (a) Photograph and (b) schematic diagram of the experimental setup of the grating

spectrophotometer to measure the emission spectrum of atomic hydrogen.

1. Set up the experiment equipment as shown in Fig. 9. Align the optics properly.

2. Use the hydrogen (Balmer) source as your first source.

(NOTE: Spectrum Tube must be turned off for at least 30 seconds for every 30 seconds

usage.)

3. Using the ring stand clamps, adjust the level of the optics bench such that it is at the

same level as the light source.

4. Turn on the light source and darken the room. Use the opaque cloth to ensure that only

light from the slit reaches the collimating lens.

5. Using the largest collimating slit, make sure that the diffraction grating is perpendicular

to the incident beam by checking that the back-reflection of the incident light goes right

back to the source.

6. Adjust the light source, collimating slits and collimating lens so that clear images of the

central ray and the first order spectral lines appear on the aperture disk and aperture

screen in front of the high sensitivity Light Sensor.

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7. Align the focusing lens with the marking on the Degree Plate.

8. Turn the aperture disk so that the smallest slit on the disk is in line with the central ray.

9. On the Science Workshop 750 Interface, connect the Light Sensor to Analog Channel

A and the Rotary Motion Sensor to Digital Channels 1 and 2.

10. Use the following settings for the Rotary Motion Sensor:

a) Sample Rate: 50 Hz

b) Measurement: Angular Position, Ch 1 & 2 (deg)

c) Resolution: High (1440 divisions per rotation)

d) Linear Scale: Rack and Pinion

11. Use the following settings for the Light Sensor:

a) Sample Rate: 50 Hz

b) Measurement: Light Intensity, Ch A

12. Create a calculation of the actual angular position of the degree plate in DataStudio.

The angular position of the Rotary Motion Sensor must be divided by the ratio of the

radius of the Degree Plate and the radius of the small post on the pinion.

(The ratio is approximately 60 to 1. To do so, key in Actual Angular Position = /60

with = Angular Position, Ch 1 & 2 under Variables Data Measurements)

13. Set the GAIN select switch on top of the High Sensitivity Light Sensor to 100.

14. Scan the spectrum all the way through the central ray, and all the way through the first

order spectral lines on the other side of the central ray

15. Plot the graph of Light Intensity (% max) against Angular Position on DataStudio. (or

on Origin 8.0/MATLAB graphing software, please do not use Microsoft Excel)

16. Repeat the scan by setting different light sensor gain levels or slit widths to obtain the

best scan, or to obtain mean values of the angles needed to find the wavelengths.

17. Find the angle between the two matching spectral lines. The angle, , is half of the

angle between the two lines and use = 1666 .

18. Repeat the experiment for the other colours in the first-order spectrum.

19. Tabulate your results.

20. Compare your results with the accepted values found in;

http://hyperphysics.phy-astr.gsu.edu/hbase/hyde.html

21. Comment on your results.

http://hyperphysics.phy-astr.gsu.edu/hbase/hyde.html

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Part III (Optional): Identification of Unknown Vapours using the Grating

Spectrophotometer

1. Using procedures similar to those in Part II, identify the unknown spectral tubes

labelled l.

2. Compare your results with the accepted values.

3. Comment on your results.

4. You may identify more tubes if you have time.

Recommended Readings

Young Freedman 13th edition, University Physics with modern Physics, Chapter 39

Energy levels and the Bohr Model of Atom; Chapter 41, Atomic Structure

Serway & Jewett, Physics for Scientists and Engineers, 8th edition. Chapter 42:

Atomic Physics

HyperPhysics, Hydrogen Energies and Spectrum.

http://hyperphysics.phy-astr.gsu.edu/hbase/hyde.html#c4

HyperPhysics, Atomic Spectra.

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/atspect.html#c1

National Institute of Standards and Technology, NIST Atomic Spectra Database.

http://www.nist.gov/pml/data/asd.cfm