Experiment: CD Diffraction

The purpose of this experiment to analyze the diffraction pattern that results from a CD being stuck with a laser.

Equipment:
-Laser
-CD
-Large screen with small central hole
-Meter stick
-Stands and clamps

In this experiment, we arranged the laser, screen, and CD so that the laser shinned through the hole in the screen and struck the CD perpendicularly on the recordable side.

 

When the beam struck the disk perpendicularly at the grooves, the first order maxima appeared on the screen on both sides of the hole. We then measured our x and L distanced and analyzed the diffraction pattern to calculate the distance between the grooves on the CD. 

 Our measure value for the distance between the grooves on the CD was 1535 nm. The accepted value given by the manufacturer is 1600 nm.

The percent error is = (1600-1535)/(1600)*100% = 4.06%

This percent error could have come from the fact that the observed maximas we big blurred dots which meant that we estimated the distance between the first maxima and the center of the laser ray.

Experiment: Width of a Human Hair

The purpose of this experiment was tho measure the thickness of a a human hair.

Equipment:
-Laser pointer
-3x5 card with hole punched
-Human Hair
-Whiteboard

In this experiment we taped a human hair across the hole of a 3x5 card and clamped the card parallel to the wall several meter away from the whiteboard. We then mounted the laser so that it pointed perpendicularly toward the whiteboard through the hole in the card. We then turned on the laser and adjusted the card so that the beam went right through the hair. This then produced a diffraction pattern on the whiteboard. We then measured the distance between the minimas.

(The picture above shows the beam going through the hole in the card)

(This picture was the diffraction pattern on the white board that we analyzed)

Below is our data and data analysis:

Experiment: Lenses

The purpose of this lab was to explore the type of images that are formed at different abject distances and develop a relationship between the object distance and the image distance.

Equipment:
-Optics Bench
-Light
-Object
-Lens and lens holder
-Whiteboard

First we determined the focal length of the lens by using a distant object such as the sun to find a convergance at a focal point. We determined the focal point pf our lens to be 8 cm.

We then set up our apparatus (below) and we varied the position of the object, lens, and the image screen and tabulated the image height, magnification and the type of image that we viewed.

Below is the data:

When we changed the object distance to .5f (4cm) there was no image. This was because at this point it was a virtual image. If you looked through the lens at the object and viewed the image, you could see the image but it was magnified.

We then plotted a graph of the image distance vs the object distance using centimeters.

We then created a new column of data for the inverse image distance and the negative inverse object distance and plotted a graph of the inverse image distance vs the negative inverse distance.

This graph's slope is y=1.027x+.1099. The y-intercept of this graph is the inverse focal length of the lens that we used. Therefore, the theoretical focal length is 9.11 cm.

The percent error for our focal length is: % Error = (9.11-8)/9.11 * 100% = 12.2%.

This percent error could have come from the fact that we used the sun to find the focal length of the lens, but it was a very gloomy day so taking the measurements of the focal length using the sun were not accurate.

Experiment 7: Introduction to Reflection and Refraction

The purpose of this lab was to study the properties of reflection and refraction using semicircular prism and a source of light.

In this experiment we used:

- Light box

- Semicircular prism

- Protractor

PART ONE:
First we adjusted the light box so that the light waves entered the flat part of the semicircular and exited the curved part. We taped a paper protractor under it so that the center of the flat side was on top of the protractor and on the 0 and 180 degree line. We then turned on the light box and recorded the angle of incidence θ1 and the angle of refraction θ2. We then rotated the prism  and protractor (together) by 4-8 degrees and measured the angles. We did this for a total of ten trials until we reached 80 degrees.  

 

Below is the data collected:

We recorded the values for theta1 and theta2 and found the sin(theta1) and sin(theta2). We then plotted the sin(theta1) vs sin(theta2). 

 The slope of this graph was 1.9944. This slope is the index of refraction of the material that we used. 

PART TWO:

In this part of the experiment we did the same as above except that the light box ray entered the curve part of the semicircular prism and exited the plat side. We recorded the theta1 and theta2 when it was at 0 degrees and then rotated the prism every 4-8 degrees.

We recorded the values for theta1 and theta2 and found the sin(theta1) and sin(theta2). We then plotted the sin(theta1) vs sin(theta2). 

 The slope of the plot is 1.3346 is the index of refraction of the semicircular prism. We were not able to complete all of the trials because at 45 degrees, there was the critical angle where there was no refracted ray.

Conclusion:

The theoretical value for the the index of refraction of the semicircular prism is 1.49.