Experiment 10: Lenses

The purpose of this lab is to observe characteristics of images on the other side of a converging lens.

Method: 

We found the focal length of a lens by using the sun, a ruler and piece of cardboard.  The distance to get a bright dot on the cardboard as the lens faces the sun is the focal lenth, which was determined to be 4.2cm.  A lamp with a filament of a distinguishable shape projects a image though the lens to a piece of cardboard..  The Distance for the lens to the filament (d­­­₀) and the distance from the lens to the image(d_i) was measured.  The filament width (h₀) and the image width (h_i) were measured.  For objects too big, the width of the center was used.  These were used to calculate the magnification.  This process was repeated for several distance of the focal length.

Data

do(cm)	di(cm)	ho(cm)	hi(cm)	M	Type of image	inverse di(cm^-1)	inverse -do(cm^-1)
21	6.3	8.8	3	0.34	Real	0.158730159	-0.047619048
16.8	6.9	8.8	3.5	0.39	Real	0.144927536	-0.05952381
12.6	8.9	8.8	6	0.68	Real	0.112359551	-0.079365079
8.4	14.6	1.1	2.2	2	Real	0.068493151	-0.119047619
6.3	34.8	1.1	5.9	5.4	Real	0.028735632	-0.158730159

Analysis

When image is displayed on the cardboard it is real and inverted both vertically and horizontally.  Since the lense is convex on both sides, the image will not change if we reverse the lens.  If you cover half the lens, the whole image still shows but dimmer and more blurry because any point on the lens can produce the image.  If you change the object distance to 0.5f you can not see a real image anymore.  However, you can see a virtual one in the lens.  The image is upright.

Graph d­₀ vs.d_i

Graph negative inverse d­₀ vs.inverse d_i

Slope = 1.18 y-intercept = 0.212

The y intercept is the inverse of the focal length.

We proved 

Experiment 9: concave and convex mirrors

The purpose of this experiment is to explore images formed by concave and convex mirrors.

Convex

The image is smaller and upright.  The object looks farther in the mirror. As you move closer to the mirror, the image becomes normal size.  As you move farther the object becomes much smaller.

Convex Worksheet

The magnification is 2.2cm/.8 =.37

The magnification of the real convex mirror is taken by dividing the measured the image height by the object height. 

6.2cm/12cm=.517

Concave

The image appears larger and upright. As you move closer to the mirror the image returns to normal.  If you move the object far enough the image is large and upside down. 

Concave Worksheet

The magnification is 2.2cm/.8 =.37

The magnification of the real convex mirror is

21.5cm/12cm=1.79

Experiment 7: Introduction to Reflection and Refraction

The purpose of this experiment is to study the effects of a light ray as they pass though  a semicircular piece of plastic.  Light is bent because of the plastics index of refraction.

The Flat Surface

The first case is the angle of incidence is perpendicular to the flat surface.  There is no initial angle of refraction.  As the light ray leave the plastic the light will be refracted because of the change in medium form low density air to high density plastic.

Trial	θ1 deg	θ1 rad	θ2 deg	θ2 rad	Sinθ1	sinθ2
1	0	0	0	0	0	0
2	5	0.087266	3	0.05236	0.087156	0.052336
3	10	0.174533	6	0.10472	0.173648	0.104528
4	15	0.261799	9	0.15708	0.258819	0.156434
5	20	0.349066	12	0.20944	0.34202	0.207912
6	23	0.401426	15	0.261799	0.390731	0.258819
7	30	0.523599	13	0.226893	0.5	0.224951
8	35	0.610865	22	0.383972	0.573576	0.374607
9	40	0.698132	27	0.471239	0.642788	0.45399
10	45	0.785398	29	0.506145	0.707107	0.48481
11	50	0.872665	32	0.558505	0.766044	0.529919
12	60	1.047198	34	0.593412	0.866025	0.559193
13	70	1.22173	39	0.680678	0.939693	0.62932

Graph

θ­₁ vs θ­₂

A line equation fits this curve.

sin θ₁ vs sinθ­₂

The line equation is 1.43x+0.036.  The slope is the medium1/medium2 the y intercept suppose to be zero.

Curved Surface

The light ray hits the curved surface first.  When it hits the semicircle in initial position the light comes out un altered.  As angle increases the refraction increases. There will be an angle where the light will be internally refracted.

Trial	θ1 deg	θ1 rad	θ2 deg	θ2 rad	Sinθ1	sinθ2
1	0	0	0	0	0	0
2	3	0.05236	5	0.087266	0.052336	0.087156
3	6	0.10472	10	0.174533	0.104528	0.173648
4	9	0.15708	15	0.261799	0.156434	0.258819
5	12	0.20944	20	0.349066	0.207912	0.34202
6	15	0.261799	23	0.401426	0.258819	0.390731
7	13	0.226893	30	0.523599	0.224951	0.5
8	22	0.383972	35	0.610865	0.374607	0.573576
9	27	0.471239	40	0.698132	0.45399	0.642788
10	29	0.506145	45	0.785398	0.48481	0.707107
11	32	0.558505	50	0.872665	0.529919	0.766044
12	34	0.593412	60	1.047198	0.559193	0.866025
13	39	0.680678	70	1.22173	0.62932	0.939693
14	42	0.733038	90	1.570796	0.669131	1

When the angle of incidence reached 42 degrees the light did no come out.  The light was internally refracted.

Graph

sin θ₁ vs sinθ­₂

The equation is not the same.  The slope is the inverse relationship of the first equation.

Experiment 6: Speed of sound

The purpose of this experiment is to find speed of sound by closed pipes and reflected waves. Sound waves are compression waves that can be reflected back through a pipe.

The speed of sound is the time it takes for the wave to travel the length of the pipe.

Procedure

We performed this experiment by snapping our fingers at the end of a closed pipe and recording the sound of its echo.  We take the time difference between the original wave and the beginning of the reflected wave.  The length of the pipe is 1.32m, but since the wave is reflected it travels twice that length.  The speed of sound is found by the equation  

 In our case 

The data

Trial	Time original wave (s)	Time reflected wave (s)	Time difference (s)	Speed(m/s)	% error
1	0.00426	0.01124	0.00698	378.22	10.08
2	0.00074	0.00736	0.00662	398.79	16.06
3	0.00062	0.00776	0.00714	369.75	7.61
4	0.00078	0.00814	0.00736	358.70	4.39
5	0.0007	0.0076	0.0069	382.61	11.35

The actual speed of sound used for error is v =331+0.60T. T is room temperature. If lab room temperature is 21⁰C, then the speed of sound is 343.6m/s.  This speed is used for error.

Summary

Our measurements for the speed of sound had large error.  It is important to use sound measurements as brief as possible because the speed of sound is big.  The error of the measured time causes big deviations in calculated speed.  If we measured from the fist smallest peak of the echo, we might have gotten better measurements.