PHYS 2426 – Engineering Physics II

Physical Optics Part 2 – Diffraction and an Application of Diffraction Gratings

Leader: _________________________	Recorder: __________________________

Skeptic: _________________________	Encourager: ________________________

Materials

Red Diode Laser	Optics bench

Green Laser Diode	Single Slit Set

Masking tape	Large Paper

Red Tide Spectrometer with Fiber Optic Cable

Laptop	Discharge Lamp with Hydrogen Tube

Diffraction Grating	Ring Stand and Clamps as needed

Safety

The lasers we are using are just powerful enough that if you took a shot directly in the eye, you could possibly damage your vision. Thus, we should take a few simple precautions to prevent the unlikely event of eye damage.

1. Never look directly into the laser beam. Laser light has a high intensity and can also be easily focused. A direct shot of the laser beam on your eye will be focused by your eye’s lens onto a small spot on your retina and can burn or possibly detach the retina.

2. Never hold an object by hand in front of the laser beam. This prevents the possibility of accidentally shining the light into your eyes.

3. Keep your head above the plane of the laser beam.

4. Whenever the light strikes an object, there will be a reflection. At times the reflections can be almost as strong as the incident beam. Know where the reflections are and block them if necessary.

5. If the laser has a shutter in front of the beam, use it. When not taking data, place the shutter in front of the laser beam. If there is no shutter then block the laser beam or turn off the laser when not using it.

Introduction

Part 2 of this lab is very similar to part 1. In part 1 we examined the patterns produced by light passing through a double slit. In part 2, we will examine the far field pattern produced by light passing through a single slit.

Procedure

I. Diffraction from a Single Slit

Procedure

1. Place the red diode laser in the optical bench and aim it towards the wall. Place the single slit set in the bench and rotate it so that the diode laser is aimed at the single slit labeled a = .16. The aperture of the slit has a width of .16 mm. Tape a sheet of white paper on the wall perpendicular to the pattern and trace the pattern onto the paper.

Q1) Describe two ways in which the diffraction pattern is different than the interference pattern.

D2) Determine the spacing between the central peak and the first minimum and use that to determine the size of the slit. Assume the wavelength of the diode laser is 650 nm. (Hint: Determine the distance between the first minimum on either side of the central peak and divide by two.) Record your data and show all of your calculations neatly organized in the space below.

Q3) Rotate the slit to the next smaller size. Describe qualitatively how the pattern changes.

Q4) Rotate the slit to the next smaller size. Describe qualitatively how the pattern changes

Q5) Rotate the slit to the next smaller size. Describe qualitatively how the pattern changes

Q6) In general, how does the diffraction pattern change as you go to smaller slit sizes?

Aim the green diode laser at the slit labeled a = .16. Trace the pattern onto a sheet of paper.

Q8) Compare the pattern produced by the green laser to that produced by the red laser. How is it similar and how is it different?

D9) Determine the spacing between the central peak and the first minimum. Use that spacing and the width of the aperture to determine the wavelength of the green diode laser. Record your data and show your calculations in the space below.

Part II Application of Diffraction Gratings to the Measurement of Atomic Spectra

A very common application of diffraction gratings is to use them as the dispersive element in a spectrometer. A spectrometer measures the intensity of light versus the wavelength (or frequency). Spectroscopy is widely used in physics chemistry and engineering for studies of atomic structure, nuclear structure, chemical composition and so on. In this activity we will explore the visible portion of the spectrum of hydrogen atom.

The visible portion of the hydrogen spectrum consists of four lines. The hydrogen spectrum can be accurately calculated using the Rydberg formula

given by where R = 1.097 x 107 m-1. λ is the wavelength of the light, R is a constant specific to hydrogen called the Rydberg constant, and n1 and n2 are integers corresponding to the different orbitals the electron moves between when emitting the light. If n1 = 1, then the lines are all in the ultraviolet and the series of wavelengths calculated by letting n2 = 2, 3, 4, 5, .. is called the Lyman series. The visible lines emitted by Hydrogen, called the Balmer series, occur when n1 = 2 and n2 = 3, 4, 5, and 6. If n1 = 3, then the series is called the Paschen series. This series occurs in the infrared.

Procedure

1. Preliminary Observation

View the hydrogen discharge lamp with the diffraction grating.

Q10) What colors do you observe?

Q11) Based on your observations, explain why light emitted by the hydrogen lamp is often referred to as lines.

D12) Use the Rydberg formula to predict the wavelengths of the four visible lines of the hydrogen spectrum. Show your work.

2. Set Up

Connect the Redtide Spectrometer to the Computer with the USB cable. Connect the fiber optic cable to the spectrometer. Start up LoggerPro. After a brief wait, LoggerPro should detect the spectrometer. Click on the Experiment Menu, then click on Change Units and then click on Spectrometer. Click on Intensity.

2. Data Collection

Use clamps and ring stands as needed to hold the free end of the fiber optic cable next to the discharge lamp. Click on collect and record the spectrum of the lamp. If you notice that any of the peaks seem to be flat at the top, then you are saturating the detector and you need to reduce the intensity. You can accomplish this by moving the fiber optic cable away from the lamp. Repeat data collection and adjust as needed until you have a good spectrum.

Once you have an acceptable spectrum, determine the peak wavelength for each line. The red line at about 653 nm is often called Hα (read as hydrogen alpha), the blue green line is called Hβ, and so on. Record your data in the table below.

D13) Data table for measured values of the wavelength

Line	Measured	Percent Difference
Hα
Hβ
Hγ
Hδ

D14) Calculate the percent difference between the measured and the predicted values of for each of the line. Use %difference =|(predicted – measured)/predicted)|*100%