PHYS 2426 – Engineering Physics II

The Speed of Light

 

Leader: _________________________          Recorder: __________________________

Skeptic: _________________________         Encourager: ________________________

 

Materials

Pasco Speed of Light Apparatus

Concave Mirror

Tripod to hold mirror

5 m tape measure

Digital oscilloscope

2 MHz Function Generator

BNC cable

RCA – BNC cable

Phone Jack – BNC cable

Laptop for graphs

Plumb bob

masking tape

 

Safety

The lasers we are using are just powerful enough that if you took a shot directly in the eye, you could 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

      The speed of light is one of the most important physical constants.  It is the maximum speed that information can be transmitted and thus presents a fundamental limit to communication.  Using interferometric techniques, the speed of light can be measured with such a degree of accuracy that its value is now taken to be defined as 2.99792458 × 108 m/s.  This value in turn is used to define the meter.  Under current convention the meter is defined as the distance light travels in 1/2.99792458 × 108  s.

      Efforts to measure the speed of light date back to Galileo.  He sent a servant several miles away with a lantern and tried to time the lag between when he signaled the lantern to be shown and when he saw the lantern.  About all Galileo could determine was that light had a speed, but it was a beginning.  Coincidentally, Galileo’s method is not all that different from the method we will use.  We will modulate the output of a diode laser, turning it on and off at 2 MHz, send the beam across the room to a mirror, reflect it across the room again to a detector and compare the return signal to the output signal.  Because of the distance traveled by the light, the modulated laser beam will have a phase shift with respect to the source and from the phase shift, we can determine the speed of light.

 

Procedure

1.  Set up

Place the laser at one end of the optical bench and the lens and the receiver at the opposite end as shown in figure 1

 

Figure 1 Schematic of Optical Setup

 

 

 

 

 

 

 

 

 

 


Place the concave mirror on the tripod and adjust the height of the tripod so that it is the same height as the laser.  Place the tripod several meters in front of the laser then use a plumb bob and tape to mark the position of the mirror on the floor.  Mark off 1 m distances from the initial mark of the mirror out to 10 m (or you hit the back of the room).

      Connect the TTL/CMOS output of the Function generator with the BNC cable to CH 1 of the oscilloscope.  Turn on the oscilloscope.  Use the RCA – BNC cable to connect the “Video” output of the receiver to CH 2 of the oscilloscope.  Use the phone-plug to BNC cable to connect the power jack of the laser to the output of the function generator.  Set the function generator to generate a square wave and turn the output and DC offset knobs fully clockwise.  Turn the laser switch button into the “ON” position.  Turn the DC offset button up until you see light emitted from the laser.  A good way to check this is to hold a piece of paper several inches in front of the laser.  Align the laser, lens, mirror, and receiver so that laser beam is focused onto the “Video” Sensing element of the receiver.

      Press the Auto Set button on the oscilloscope.  Adjust the laser, mirror, lens, and receiver to maximize the signal on CH 2 of the oscilloscope.  Adjust the DC offset and the amplitude on the function generator to maximize the signal in CH 2.

 


3.   Data Acquisition

Adjust the horizontal sensitivity so that the phase difference between the two signals can be measured as accurately as possible.  Press the Cursor button and choose Time as the type.  Measure the Δt between the two signals.  Record the value in the data table below.

 

Move the mirror to the next 1 m mark back.  Adjust the laser, mirror, lens, and receiver to maximize the signal again.  However, don’t change the position of the receiver on the bench.  Measure the Δt and record it in the data table below.

 

Q1)  How far did you move the mirror from the first point?

 

 

Q2)  What is the additional distance the light travels?  Explain.

 

 

Record the additional path distance of the light in the data table.

 

Q3)  Did the Δt change between the first and second reading?  If so how?

 

 

Q4)  Why did the Δt increase?

 

 

Q5)  Denote the speed of light by c, the increase in distance by Δd, and the increase in time by Δt, write an expression for Δt.

 

 

Repeat the steps of moving the mirror back by 1 m, maximizing the signal, and measuring Δt until you have moved the mirror to a distance of 10 m from the starting point.  Record your values in the data table.

 

Δt

Additional path distance from starting point

 

0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Construct a properly labeled graph of Additional Path Distance vs. Δt.

 

Q6)  Do your data lie on a fairly straight line?

 

 

Q7)  Based on your answer to Q5), what should be the slope of the line?

 

 

Q8)  Add a best fit line and record the slope.  Don’t forget units.

Print and attach a copy of the report.

 

Q9)  Record the value of the speed of light determined by this experiment in SI units.

 

 

Q10)  Determine the % difference between your measured value and the accepted value for the speed of light.

 

 

Q11)  Does this method seem very accurate?

 

 

Q12)  What aspects of the experiment did you find difficult?

 

 

Q13)  How do you think the aspects that you found difficult contributed to the experimental error?

 

 

Q14)  What improvements in procedure or equipment do you think would make for a more accurate determination of the speed of light.  Explain.