Experiment 11: CD Diffraction

Purpose:

The purpose of this experiment is to measure the wavelength of a laser and to measure the distance between the grooves on CD using diffraction.

Experiment:

The wavelength of the laser can be measure using a diffraction grating.

Diffraction pattern can be seen on the board when laser passes through
a diffraction grating

The wavelength can then be calculated as follow

where: L = distance from diffraction grating to the white board
           d = width of slit on the grating
           y = distance between 2 maxima

To measure the distance between the grooves on CD, the following setup is used

Laser is reflected off of the CD and diffraction pattern is
observed on a piece of paper.

The distance between grooves can then be calculated as follow

This value gives us an error of 87% when compared with the expected value which is 1600nm

Conclusion:
Although the experiment has a really high error, we can still see that with more careful measurement, the distance between the grooves on CD can be calculated by applying the concept of diffraction. The reason of the large error in this experiment is mostly because the paper and the CD may not be exactly parallel.

Experiment 10: Measuring a Human Hair

Purpose:

The purpose of this experiment is to measure the thickness of a human hair by applying Young's double slits experiment.

Experiment:

The setup of the experiment is as follow

A strand of hair is used as the slit

Experiment setup

Using laser with wavelength of 660nm, interference pattern is projected onto a white board.

Interference Pattern

After some measurement, the thickness of the hair can be calculated as follow

Calculation of thickness of the hair

where: y = distance between 2 fringes

           L = distance between the card and the white board

           d = width of the slit

We then tried to verify this value by measuring the thickness of the same hair using a micrometer.

Measuring the thickness using a micrometer.

Thickness of hair according to micrometer: 50 ± 20μm

Conclusion:
The Young's double slit experiment can successfully be used to measure the thickness of human hair. Although the calculated value and the value measured using micrometer differ by 65%, the calculated value still falls within the uncertainty range.

Experiment 9: Lenses

Purpose:

        The purpose of this lab is to analyze the characteristic of a biconvex lens and verify the relationship between the image distance, object distance, and focal length.

Experiment:

The focal length of the lens can be found by measuring when the parallel ray from the sun passing through the lens form a single bright dot.

The following apparatus is then set up

We can then measure the image distance and image height when the image is focused on a screen and the object distance is equal to 1.5f, 2f, 3f, 4f, and 5f

The image focused on a whiteboard

Measuring image distance and image height

Data and Data Analysis:

Focal Length (f) = 4.8 ± 0.5cm

d0(cm)	di(cm)	h0(cm)	hi(cm)	M	Type of image
25	7.4	8.8	2.3	0.26	Real, inverted
20	8.4	8.8	3.4	0.39	Real, inverted
15	8.9	4.0	2.6	0.65	Real, inverted
10	11.8	4.0	4.5	1.12	Real, inverted
7.5	18.3	1.1	2.8	2.55	Real, inverted

When the object distance is changed to 0.5f, the image no longer shows up on the board, however, when looked through the lens, the image is upright. This means that the image is virtual.

Graph of d_i vs d₀

Inverse d_i vs d₀

d0(cm)	Inverse di(1/cm)
25	0.135
20	0.119
15	0.112
10	0.085
7.5	0.055

Inverse d_i vs negative inverse d₀

Inverse di(1/cm)	Negative inverse d0(1/cm)
0.135	-0.04
0.119	-0.05
0.112	-0.067
0.085	-0.1
0.055	-0.13

The lens equation shows that:

which implies that the slope of the graph above should be 1 and the y-intercept is 1/f.

We can then conclude that, according to the graph, the focal length should be:

f = 1/0.1653 = 6.0cm

From the regression line of the graph we can then conclude that:

Error Analysis:

The error on this experiment can be mostly contributed to measurement error. We can contribute an error of about ±3cm on all measurement due to the increments of the ruler used, ruler that is not perfectly perpendicular with the paper and the light source, and the image that may not be completely focused on the screen.

Summary:

From this experiment, we can conclude that the image created by a biconvex lens is real and inverted. The magnification of this lens vary with the object distance. As the object distance gets smaller, the magnification becomes larger. We can also conclude that if the object distance is smaller than the focal length, then the image produced by this lens become virtual and upright.

Experiment 8: Concave and Convex Mirrors

Purpose:

       The purpose of this experiment is to study the characteristics of the image created on a concave and convex mirror

Experiment:

Convex Mirror

Image on convex mirror from far distance

Image on convex mirror from small distance

Characteristics of image formed on a convex mirror:
1a. Image appears smaller than the object
  b. Image is upright
  c. Image distance seems to be larger than the object distance

2. When moved closer, image still has the same characteristics as above.

3. As the object gets farther away from the mirror, the image size becomes a lot smaller.

Light Ray Diagram for Convex Mirror

d₀ = 5.5cm

d_i = 1.9cm

h₀ = 2.2cm

h_i = 0.7cm

M = h_i/h₀ = 0.32

Concave Mirror

Image on concave mirror from far distance

Image on concave mirror from small distance

Characteristics of image formed by concave mirror:
1a. The image appears larger than the object
  b. The image is upright
  c. The image distance is smaller than the object distance

2. As the object moves farther, the image appears smaller than the object and it becomes inverted.

Light Ray Diagram for Concave Mirror

d₀ = 11.6cm

d_i = 3.3cm

h₀ = 2.3cm

h_i = 0.6cm

M = h_i/h₀ = 0.26

Summary:
Image formed by convex mirror is upright and smaller, while the image formed by concave mirror depends on the position of the object. If the object is in front of the focus point, the image is inverted and smaller than the object. If the object is behind the focus point, the image is upright and larger than the object.

Experiment 7: Introduction to Reflection and Refraction

Purpose:

        The purpose of this experiment is to analyze the behavior of light as it travels from one medium to another, and to find the relationship between the index of refraction, the incident angle, and the refraction angle.

Experiment Part 1:

Materials and experiment set-up. Light comes in from
the flat side of the semicircular plastic

Incident angle and refraction angle can be measured by
placing a protractor underneath the plastic

Data

Trial	θ1	θ2	sin θ1	sin θ2
1	0	0	0	0
2	10 o ± 1o	5 o ± 3o	0.17	0.09
3	15 o ± 1o	11 o ± 3o	0.26	0.19
4	20 o ± 1o	12 o ± 3o	0.34	0.21
5	25 o ± 1o	17 o ± 3o	0.42	0.29
6	30 o ± 1o	19 o ± 3o	0.50	0.33
7	40 o ± 1o	23 o ± 3o	0.64	0.39
8	50 o ± 1o	27 o ± 3o	0.77	0.45
9	60 o ± 1o	35 o ± 3o	0.87	0.57
10	70 o ± 1o	39 o ± 3o	0.94	0.63

Graph

The slope of this graph (1.5192) represents the ratio of index of refraction between the plastic and the air. Since the index of refraction of air is 1, we can conclude that the index of refraction of air is 1.5192

Experiment Part 2:
The setup in this part is similar to the first part, but light comes in from the circular side of the plastic, which means refraction only happens as the light travels from the plastic to the air.

Experiment Part 2 Setup

Data

Trial	θ1	θ2	sin θ1	sin θ2
1	0	0	0	0
2	5 o ± 1o	9.5 o ± 3o	0.09	0.17
3	10 o ± 1o	16.5 o ± 3o	0.17	0.28
4	15 o ± 1o	24.5 o ± 3o	0.26	0.41
5	20 o ± 1o	30 o ± 3o	0.34	0.50
6	25 o ± 1o	44 o ± 3o	0.42	0.69
7	30 o ± 1o	51.5 o ± 3o	0.50	0.78
8	35 o ± 1o	64.5 o ± 3o	0.57	0.90
9	40 o ± 1o	80 o ± 3o	0.64	0.98

Graph

Similarly to part 1, the slope of this line represents the ratio between the index of refraction between the plastic and the air.

Data can only be collected up to 40o because there is a critical angle at around 45o that would cause the ray to be totally internally reflected as shown.

No light is refracted through the plastic into the air, instead
it's being totally internally reflected.

Conclusion:
The ratio between the sine of the incident and the refracted angle is proportional to the ratio between the index of refraction of the two mediums at which light travels. This relationship is expressed in the Snell's Law:

n₁sinθ₁ = n₂sinθ₂

From the data gathered on part 1 and part, we can also conclude that the index of refraction of the plastic is around 1.5