Experiment 11: CD Diffraction

PURPOSE: Determine the distances between the grooves of a CD to determine if the CD will actually work by comparing to the actual manufactures standard value.

PROCEDURE:

Setup of apparatus to find the wavelength of the red laser beam. d is given as 0.001m/500lines.

Measurement of Ybright 

Using CD diffraction to find the length of the grooves on the disc by measuring the YBright

DATA AND ANALYSIS

Data measurement for the wavelength of the laser.

Calculation for the CD groove or distance, d. 

The actual and standard for all groove distances is 1600nm. Based on the experimental data, the experimental value of d with uncertainty falls within the actual value. 

CONCLUSION:

Based on the experiment, the CD can be confirmed to having the same amount of grooves as the standard CD, but there may be a possibility that the some of the grooves have been altered and scratched and prevents the CD from making the proper sound. The value of the d, gave us the distance between the grooves of the CD that helped defract the laser beam onto the screen. Using the formula and the measured wavelength of the laser which may have some probable.

Experiment 10: Measuring a Human Hair

OBJECTIVE:
 The purpose of this experiment is to measure the thickness of a single strand of hair using two methods of measurement; one through the use of a laser, and the other through a micrometer.

FORMULAS AND DERIVATIONS:

PROCEDURE:

Hole through the index card with the strand of hair

Laser beamed through the hole across and projected onto the screen. (2 meter away).

Beam of light through index card. (front view)

Image of the laser pattern on screen. Bright fringes of the beam were marked indicating maximum values of the light wave.

Measurement of hair strand through a micrometer.

DATA AND ANALYSIS:

Measurement of the distance of the average distance between  bright fringes.  Three trials were done to  find the  average value. Circled point represents the center.

CALCULATIONS:

Laser Measurement
Length (m)	λ (nm)	YBright (m)	D (µm)
2.000 ± 0.005	650 ± 6.5	0.0189 ±0.002	69.7 ± 8.2

Micrometer Measurement

Thickness of hair (µm)

70 ± 5

CONCLUSION:

Based on the experiment data it can be verified that the thickness of the hair strand can be measured by the use of laser. The theory behind the experiment is that if a laser is beamed through an open slit then the distance of the tiny slit can be measured by knowing the wavelength of the monochromatic light, length of the screen from the light source, and the distance between the light fringes. These values help find the thickness of the hair or in other words, the distance of the slit. The thickness of the hair was also measured by using a more appropriate use of measurement, a micrometer. The micrometer would provide more accurate data, since its sole purpose is to make only measurements. There are too many variables that could skew the data when using the laser beam. There needed to be more precise measurements when measuring using a laser, since there are more variables that need to be considered. However, although there are many differences in both ways of measuring, the thickness of the hair between the two measurements came out to be approximately the same. The advantages to the laser measurments  

Laser Measurement

Length (m)

λ (nm)

Y_Bright (m)

D (µm)

2.000 ± 0.005

650 ± 6.5

0.0189 ±0.002

69.7 ± 8.2

Micrometer Measurement

Thickness of hair (µm)

70 ± 5

Laser Measurement

Length (m)

λ (nm)

Y_Bright (m)

D (µm)

2.000 ± 0.005

650 ± 6.5

0.0189 ±0.002

69.7 ± 8.2

Micrometer Measurement

Thickness of hair (µm)

70 ± 5

Experiment 8: Concave and Convex Mirrors

PURPOSE: The purpose of the experiment was to see the images with the use of both a convex and a concave mirror. Using these mirrors the magnification and the how the image is displayed was observed to verify the effects of both a convex and concave mirror.

PROCEDURE:

Convex Mirror

Concave Mirror

Observing the effects on an image for both the concave and convex mirrors

Verifying if the image is being inverted or staying erect.
Concave-inverted
Convex-erect

Observation of the magnification in a Concave mirror

Observation of the magnification in a Convex Mirror

DATA and ANALYSIS:

Convex Mirror

Concave Mirror

Ray Diagram Concave Mirror

Ray Diagram Convex Mirror

CONCLUSION:

In the experimental observation, the convex mirror displayed images that were smaller than the original object and showed the image upright. As the object moved farther away the image became even smaller and larger when closer to the mirror. The image is considered a virtual image however since the rays as shown in the diagrams, did not pass through the image. Therefore convex mirrors displays a virtual image that is upright and is magnified smaller.

The observations for the concave mirror were somewhat different. Referring to the diagram of the concave mirror, as the object distance is larger, the image becomes inverted. When the object distance is just the same as the radius of curvature, C, both the object distance and image distance are the same. The image would not show if the distance was the same as the focal length. If the object was less than the focal length the image would be considered virtual and erect since the rays did not pass through the image. 

The magnification verifies the experiment by the showing of signs proving if the image was inverted or virtual. Based on the data, the observations and the magnification calculations both agree within terms and explains the phenomena between concave and convex mirrors. 

Experiment 9: Lenses

PURPOSE: To observe and verify the relationship between the object distance and the image distance through a mathematical relationship.

PROCEDURE:

Convex lens used in the apparatus for the experiment 

Setup of the apparatus with convex lens between the object and the image projection.

Image of the object displayed at some distance from the lens

image displayed inside the lens when object is 0.5f  from the lens.

DATA & ANALYSIS:

Focal point was determined to being 5.3 cm for the lens.

Focal distance	Object Distance cm	Image Distance cm	Object Height cm	Image Height cm	Magnification	Type of Image
5f	26.5 ± 0.3	7 ± 0.3	8.8 ± 0.1	2.3 ± 0.05	0.261363636	Diminished;Inverted; real
4f	21.2 ± 0.3	7.7 ± 0.3	8.8 ± 0.1	2.9 ± 0.05	0.329545455	Diminished;Inverted; real
3f	15.9 ± 0.3	8.4 ± 0.3	8.8 ± 0.1	4.6 ± 0.05	0.522727273	Diminished;Inverted; real
2f	10.6 ± 0.3	11.5 ± 0.3	8.8 ± 0.1	9.1 ± 0.05	1.034090909	Same; Inverted; real
1.5f	7.95 ± 0.3	15.95 ± 0.3	8.8 ± 0.1	16 ± 0.05	1.818181818	Magnified;Inverted; real

If the object distance was set to 0.5f the image no longer appears on the screen and instead is displayed on the lens itself and is also no longer inverted and instead erect. The image is therefore considered virtual since it is displayed on the object side.

With the best fit line an equation, y= mx+b is found with a slope of .9038 and a y-intercept 0.1748. The y intercept is the inverse of the focal length.

Measured focal length	Y-intercept focal length
5.3 cm ± 0.5	5.72 cm

CONCLUSION:

The magnification had increased as the focal distance decreased until the object was less than the focal distance which created a a virtual image and thus did not show up as a projection on the piece of paper.          
The lens used was a converging lens inverting the image onto the piece of paper creating a real image of the object. However, again the image was erect in the lens when the object distance was .5f, creating a virtual image. Graph 1 shows the relationship between the image and the object distance verifying that there was an inverse relationship. Graph 2 represented a different approach to view the relationship between the object distance and the image distance. A negative inverse and and inverse image distance was graphed and the y-intercept that was found from the linear graph equaled to the inverse of the focus length. The measured focal length that was used by the suns ray was about 5.3 with an uncertainty of about ± 0.5. With this uncertainty the y-intercept or focal length is within the value of uncertainty indicating that the relationship between the image distance and object distance is verified with the following equation

Experiment 7: Introduction to Reflection and Refraction

PURPOSE: The purpose of this experiment is to verify the properties that are related to reflection and refraction using two mediums to reflect and refract a beam of light.

FORMULAS AND DERIVATIONS:                        

PROCEDURE:

Setup of the light beam with protractor underneath semicircle glass medium.

Measurements of different angles at different angles of light beams.  

Reversing the semicircle and recording the refraction angles again.

DATA & ANALYSIS:


Before the experiment, there were some predicted results and phenomena that were expected. The angle of incidence for the light ray at the flat surface would be zero and the angle of refraction at the flat surface would also be zero as well. As the light ray leaves the plastic piece at the curved edge and goes into the air the light will travel straight out since the light ray travels straight as it comes in. In the first situation light travels from a lower density to a higher density. These predictions were verified after turning on the light observing the results.

Trial 1
θi	Error	θr	Error	Rad(θ1)	Error	Rad(θ2)	Error	sin(θi)	Error	sin(θr)	Error
10	± 1	7	± 1	0.1745	± 0.017	0.1222	± 0.017	0.1736	±0.841	0.1219	±0.841
15	± 1	10	± 1	0.2618	± 0.017	0.1745	± 0.017	0.2588	±0.841	0.1736	±0.841
20	± 1	12	± 1	0.3491	± 0.017	0.2094	± 0.017	0.3420	±0.841	0.2079	±0.841
30	± 1	21	± 1	0.5236	± 0.017	0.3665	± 0.017	0.5000	±0.841	0.3584	±0.841
40	± 1	24	± 1	0.6981	± 0.017	0.4189	± 0.017	0.6428	±0.841	0.4067	±0.841
45	± 1	32	± 1	0.7854	± 0.017	0.5585	± 0.017	0.7071	±0.841	0.5299	±0.841
50	± 1	28.5	± 1	0.8727	± 0.017	0.4974	± 0.017	0.7660	±0.841	0.4772	±0.841
60	± 1	35	± 1	1.0472	± 0.017	0.6109	± 0.017	0.8660	±0.841	0.5736	±0.841
70	± 1	39	± 1	1.2217	± 0.017	0.6807	± 0.017	0.9397	±0.841	0.6293	±0.841
80	± 1	40	± 1	1.3963	± 0.017	0.6981	± 0.017	0.9848	±0.841	0.6428	±0.841

For the 2nd Trial there were also predicted results that were stated. As the light ray hits the first curved surface of the semicircle prism, the light ray goes through as a straight light. This would occur because both the angle of incident and angle of refraction is zero. When the light ray comes out the flat surface there will be a refraction as it goes into the air. The experiment will has a situation where light travels from a higher density to lower density.

TRIAL 2
θi	Error	θr	Error	Rad(θ1)	Error	Rad(θ2)	Error	sin(θi)	Error	sin(θr)	Error
6	± 1	10	± 1	0.0960	± 0.0174	0.1745	± 0.0174	0.0958	±0.8414	0.1736	±0.8414
11	± 1	15	± 1	0.1920	± 0.0174	0.2618	± 0.0174	0.1908	±0.8414	0.2588	±0.8414
12	± 1	20	± 1	0.2094	± 0.0174	0.3491	± 0.0174	0.2079	±0.8414	0.3420	±0.8414
19	± 1	30	± 1	0.3316	± 0.0174	0.5236	± 0.0174	0.3256	±0.8414	0.5000	±0.8414
23	± 1	40	± 1	0.3927	± 0.0174	0.6981	± 0.0174	0.3827	±0.8414	0.6428	±0.8414
26	± 1	45	± 1	0.4538	± 0.0174	0.7854	± 0.0174	0.4384	±0.8414	0.7071	±0.8414
29	± 1	50	± 1	0.5061	± 0.0174	0.8727	± 0.0174	0.4848	±0.8414	0.7660	±0.8414
32	± 1	60	± 1	0.5585	± 0.0174	1.0472	± 0.0174	0.5299	±0.8414	0.8660	±0.8414
34	± 1	70	± 1	0.5934	± 0.0174	1.2217	± 0.0174	0.5592	±0.8414	0.9397	±0.8414
38	± 1	80	± 1	0.6632	± 0.0174	1.3963	± 0.0174	0.6157	±0.8414	0.9848	±0.8414

Slope of the line gives the ratio of the index of refraction of the two mediums

The inverse of the glass and air gives the inverse of the slope, thus an inverse ratio of the index of refraction between the two mediums.

Maximum Angle

42˚

There was also a trial to see at what point the angle of refraction becomes 90 degrees or in others others, not being able to see the light beam itself. This is also known as the critical angle and can only be obtained when there light traveling from an object with a higher index of refraction to an object with a lower index of refraction. The maximum value for the angle of refraction was recorded to being 42˚± 1. Using the law of refraction again and setting the second angle to 90 degrees gives us the equation θ_critcal=sin^-1(N_b/N_a). This equation can be used to verify the maximum angle value that was found in the experiment.

         

Theoretical Calculations:

Using the theoretical of refraction of 1.5 for glass, the experimental value of the maximum angle could be verified. The theoretical value of the critical angle was about 42 degrees which gives an exact value of the value from the theoretical. 

CONCLUSION

Using the law of refraction, N₁Sin(θ₁)=N₂Sin(θ₂), and setting θ₁ as the incident ray and θ₂ as the angle of refraction, we can set the equation as Sin(θ₁)/ Sin(θ₂)= N₂/N₁. The slope of the line can also be written as Sin(θ₂)/Sin(θ₁). Using the data of the first trial we can see that the slope is 0.6588, which is also equal to N₁/N₂. By setting the index of refraction of air to being 1, we can clearly see that N₂ = 1.52, and that it represents the index of refraction of glass. While N₁ represents the index of refraction of air with an integer value of 1. Similar results occur for trial two when the semicircle is reversed and the N­₁ is now the index of refraction of glass and N­₂ represents for the air. The slope of the given line in trial 2 gave a value of 1.6458. The percent difference between the two index of refraction for glass is about 7%. It can be verified that the two slopes of these graphs are inverses of ratio to each other. The critical angle formula was also verified by finding the maximum angle at which the light beam can refract in a situation where there is a higher index of refraction to a lower one. This can be verified because the ratio can never be greater 1 for an inverse sin value. The angle of refraction at or past the critical angle becomes 90 degrees and so it cannot be measured because  it cannot be seen. The relationship between the reflection and refraction as well as the critical angle was all verified using two mediums, glass and air. 

Maximum Angle

42˚