CD Diffraction

CD Diffraction

Objective

The objective of this lab is to determine the size of the grooves that are located on a CD or DVD

Procedure

Equipment:

Laser

Compact Disk

Meter Stick

A Screen with a hole in the middle.

Set up Diagram

Using a Screen with a hole through it arrange a laser such that it hits the surface of the CD perpendicularly.Move the CD around as needed in order to see a diffraction pattern coming from the CD to the screen. Make it so that the first order maxima will appear on the screen on either side of the hole the  laser is coming through. Measure the distance from the screen to the CD and record the distance between the maxima on the screen from the resultant diffraction pattern. for the laser used λ=633 nm the Length L=3.8 ± 0.02 cm  and the distance between maxima was    2x= 2.5 ± 0.1 cm

Calculations

Using these calculations it is seen that our error is high from the standard manufacturer's standard value of 1600 nm. This error is due to the the fact that our experiment was not stable. We couldn't get the diffraction to show on our screen so for the experiment we held the CD (off the table) in order to get the diffraction to show on the screen. As a result our measurements were not very accurate because the CD was moving around slightly.However within our uncertainty we came up with a 9.31% deviation from the standard value.

Active Physics

Relativity

 In this experiment light is going in the same direction as motion.

The time measurement of a round trip for the ray in the lights frame is independent of weather the light clock is moving relative to the earth or not.

The round trip time interval as measured on a stationary point on the earth will be longer than the frame of reference of the time clock.
The light clock shrinks in the second frame. If it didn't and the lengths in both frames were the same, then the the the dime dilation relation couldn't hold true.

If the length of the light clock were 1000m (propper length) to find the length in the second frame we can use the relation, the length in any frame is given by the proper length divided by the Lorentz Factor. If the Lorentz factor were 1.3 the the length of the clock in the second frame would be(1000)m/1.3=769m

Measuring Hair Thickness

Objective

To measure the thickness of a human hair using both laser interferometry and  a micrometer.

Equipment:
Laser
Meter Stick
Note Card
Hair
Micrometer

Procedure

Laser and note card setup

Laser

Measurement of x

First a hole was punched into the note card and a strand of hair placed tightly across it. A flat surface (a white board) was set up parallel to the note cards surface. The distance L to the surface from the note card was then measured. A laser with wavelength 633 nm was used to shine at the hair, this created a diffraction pattern that was seen on the surface. The distance between the first maxima and the second in the diffraction patter, x, was recorded. the equation,

 d=λLm

     x

was used to determine the thickness of the hair using the known values of wavelength and m and the measured values x and L

The measurement obtained from this  was compared to the measurement obtained from measuring a hair with a micrometer.

The Length of separation was 1.00 ± 0.01m
     Sample 1: y= 3.1 ± 0.1cm
                    m=6
                      Diameter = 0.000123 ± 0.000005 m
     Sample 2: y= 3.3 ± 0.1cm
                    m=4
                      Diameter = 0.0000767 ± 0.0000032 m
     Sample 3: y= 1.2 ± 0.2cm
                    m=1
                      Diameter = 0.0000528 ± 0.00001.11 m

Micrometer Measurement

     The diameter measured was on the correct order of magnitude as expected(based on values found on a scientific website) of the diameter of hair. Using the micrometer was slightly difficult but it gave similar values. For sample 1 the micrometer gave a value of 0.0002 m. This is a %error of 48%. The  micrometer is less accurate because the minimum increment of measurement is a tenth of a millimeter  The laser method can better measure small lengths because it can more accurately measure the parameters needed and obtain much smaller values.

Active Physics

Relativity

The length traveled by the light is longer in the second frame of reference .

since the speed of light is constant in all frames of reference the time it takes in the second frame of reference to complete a cycle is longer than the time in the initial frame. If the mirrors are moving at a speed where gamma=1.4 the time difference is 2.73 µs.

In the frame of reference of the time clock, the time required to complete a round trip is independent of whether the mirrors are moving or not.

The difference in light pulse travel time between the earth's timers and the light clock's timers will decrease as the time clock's speed slows down and becomes closer to that of earth's.

The equation for this effect (time dilation) is Δt = γΔtproper where the proper time is the time in the frame of the light clock. for γ = 1.2 the time seen in the second frame should be 8.00 µs which agrees with the experiment when changing γ to 1.2.

If the time for the observer in earth's frame is 7.45 µs then using the same equation we get gamma to be about 1.12. When the program is used and 1.12 is used then the timing on the earth's frame is consistent with this.

Lenses

Lenses

Objective:

 To observe characteristics of a converging lens when the object is placed on one side of the lens and the real, inverted image is placed on the other side of the lens.

Equipment:
socket lamp with V-shaped filament
Large converging lens
masking tape
Lens Holder
piece of cardboard (or other flat surface)
Track for lens
Meter stick

Procedure: 

     The focal length was recorded by taking a source that was "infinitely" far, the sun was used in this experiment because in comparison to the lens it is infinitely far away and arranging it around to find a point where the image was focused. A meter stick was used to find the distance between the lens and the focused image. This was 0.0485 ±0.0030 m.

 The following was set up by placing the lens into the lens holder and creating a track for the lens (using a meter stick and some stands). 

     The length of the arm of the image from the circle to the end of the line was take as the object image (9.2±2.0 cm). We place the image about 1.5 focal lengths away and used the cardboard to focus the resulting image. The image height and distance from the lens was recorded. From this the magnification could be found by dividing the image height by the object height. (If the lens was rotated the image remained the same). The image was always inverted.This was repeated for various multiples of the focal length.

All of these values were measured in cm. The object distance and image height values were plus or minus 0.2cm while the image distance was about plus or minus 1.5cm.

Data Analysis:

 If the object was at a distance that was less then one focal point the object height was too large to distinguish. A graph of image distance vs object distance was made and showed a nonlinear relationship. But when we graphed the inverse of negative object distance vs the inverse of image distance we got a somewhat linear relation within the given error. Do to it being an outlier the fifth data point was removed from the calculation of the plot.

 Video of focusing image.

The y intercept was 0.2208 which represents the inverse of image distance as the object distance reaches infinity. This is the inverse of the focus. The relationship between Inverse object distance (x) and inverse of image distance (y) is given in the equation in the above image.

Mirror lab

Objective:

 Explore the images formed by convex and concave mirrors.

Equipment:

Convex mirror
Concave mirror
An object
Ruler

Procedure:

This lab involved the examination of two types of mirrors, concave and convex.

     convex mirror-

 A marker was placed in front of the convex mirror.The image appears smaller than the actual object but the object is upright. The image seems further from the mirror then the actual object.        With a ruler placed normal to the mirror's center  we held the mirror a distance of 0.50m. The height of the marker (our object) was 0.12m. Measuring the size of the image of the marker gave us 0.067m when the object is moved closer increases in size and when moved further decreases.

  concave mirrors

the object was now placed in front of a convex mirror. The object appeared larger and iverted. When the object moved closer it appears upright, and still magnified. The image also appears closer to the mirror then the actual object. Using the ruler  we again placed it 0.50m from the center and we observed an inverted height of 0.21m.

Analysis:

 This phenomenon can be explained by using a diagram of light rays being reflected off the pen.
 For the convex mirror you see that the point where these rays intersect is where the top of the marker's image appears and this agrees with our observation

Concave Ray Diagram

For the concave mirror we see the focus and center of the sphere is outside of the mirror. Using the rays it can be seen that the object appears to be inverted which also agrees with our observation.

Convex Ray Diagram

From this it can be concluded that the image size and orientation depend on the focus or center of the spherical mirror.

Refraction

Refraction

Objective: 

To find a relationship between the angle that the light enters a medium and the angle at which the light is refracted by traveling through the medium. 

Equipment:

Light Box

Light box or Laser

Semicircular plastic or glass prism

circular protractor (or some way of measuring the incident and refracted angles)

Light box plus protractor

Procedure:

In performing this experiment a light box with a small slit was set up with a beam of light aimed at a semi-circular prism. A paper protractor was used to determine the angle at which the light entered to prism as well as with which angle it exited the prism. This was done by increasing the initial angle, (angle of incidence), by small increments. And recording the resultant exiting angle. Two cases were observed, the first with the incident angle at the flat surface and the second case being with the incident angle at the curved surface. The sines of the data gathered was then graphed to analyze the data.

Case 1

Sintheta1 vs sine theta 2

Case 2 

sintheta 1 vs sintheta 2 

Analysis:

TIR

In both case 1 and 2 it can be observed that the slope of the graph is equal to the ratio of the speed of light in the medium and the speed of light in air. this is also known as the index of refraction. However in case two after surpassing a certain angle total internal reflection is observed, TIR. This happens when the exiting angle, angle of refraction has exceeded 90 degrees, the angle of incidence at which this phenomenon occurs is known as the critical angle.