Experiment 5 introduction to reflection and refraction

Purpose:

the purpose of this lab is about a introduction to reflection and refraction, and we need to find what is relationship between incidence angle and reflection angle, also what is the relationship between the incidence angle and refraction angle. and how do the density of the medium affect the angle.

Equipment:

Light box or laser, Semicircular plastic or glass prism, Circular protractor, pasco optical kit or hardtl disk ( a master for a circular protractor is provided at the end of this exploration if needed)

Experiment and Data:

first part the the experiment, we use light strike at the flat surface of the semicircular plastic, and then we change the angle everytime by around 10 degree until 70 degree to get the incidence angle and the refracton angle, and calcualte sine value.

tray	Incidence angle	Refraction angle	Sin incidence angle	Sin refraction angle
1	0	0	0	0
2	5	2	0.087	0.035
3	10	7	0.174	0.122
4	18	11	0.309	0.191
5	26	13	0.438	0.225
6	34	21	0.559	0.358
7	42	25	0.669	0.432
8	50	30	0.766	0.500
9	60	35	0.866	0.574
10	70	40	0.940	0.643

then we make two graph, one is graph of incidence angle vs refraction angle, and we get all the points make a straight line, the equation of the line equation is y = 0.5825x + 0.0504

the second graph , is sin incidence angle value vs sin refraction angle value, and all the point are also make a straight line, the equation of the equation is y = 0.6771x - 0.0184

subsitute the variables of graph of sin(sita1) vs sin(sita2), we get sin(sita2) = sin(sita1)*0.6771

the slope of the graph is 0.6771 which is equal to the index of the plastic semicircular divide the index of the air.

second part of this experiment, we set up a new arragnement of the equipment, we rotate the semicircular plastic reversed, so that the light ray strikes the curved surface first. the center of the flat surface must be aligned with the center of the protractor, with the flat surface along the line of zero degree to 180 degree on the protractor. then we collect the angle of incidence angle and the reflection angle, and calculate the sin value of the two angle.

tray	Incidence angle	Refraction angle	Sin incidence angle	Sin reflection angle
1	0	180	0	0
2	8	168	0.139	0.208
3	16	156	0.276	0.407
4	24	140	0.407	0.643
5	32	127	0.530	0.799
6	40	105	0.643	0.966
7	48	147	0.743	0.731
8	56	56	0.829	0.829
9	64	65	0.899	0.906
10	70	70	0.940	0.940

we are not able to complete all 10 trials, at the first the when the incidence angle is small, we can see the refraction light out of the plastic semicicular, but when the incidence angle reach a specfic larger angle, we will not see the refraction light out of the plastic semicicular, we can only find the reflection light. in our experiment, the situation happne start at angle 48 degree and above.

we plot sin incidence angle and sin reflection angle in to excel, we get a graph separate into two parts, and each part is a straigt line, the two part of the graph separate at the point 0.643, 0.966. and we get can get from the data and graph is the first part of the graph the light do refraction in from the plastic to air, and second part of the graph light od reflection and for the reflection the incidence angle and reflection angle are the same

Conclusion:

from the experiment we get, for reflection, the incidence angle and reflection angle are always the same, and for refraction, the incidence angle and reflection have a relationship between sin incidence angle and sin refraction angle. sin(sita1)/sin(sita2) = n2/n1, and n is the index of refraction of an optical material, n = c/v, v is the speed when light go through the medium. if the light come from the smaller index to a larger index, it will always have refraction light and reflection light, and refraction light isthe main part. if the light come from the larger index to a smaller index, at the beginning when the angle of incidence is smaller, it has both refraction light and reflection light. but when the angle of incidence is get larger to a specific angle, then the refraction angle will become 90 degree which is the largest refraction angle. if the incidence angler continue to increase. we will not see the refraction ange. we can only see the reflection light.

Experiment 4 wave(2)

Purpose:




the purpose of this lab is to analyze the element of wave, such as wavelength, frequency, wave speed, tension, and period. and figure out what is the relationship among then. how does these element affect the wave.


Experiment Equipment:


Pasco Variable Fequency Wave Driver with string, Pasco Student function generator, counterweight, pulley, digital multimeter, 1 or 2 meter stick, short rod.



Experiment Data:


we measure the length of the string: 1.53 m, the weight of the string is 1.8 g = 0.0018 kg.


so we get the linear density of the string u = 0.0018kg / 1.53 m = 0.00117 kg/m


then the experiment divide into two part in different tension



we use counterweight is 300 g = 0.3 kg, T1 = 0.3 * 9.8 = 2.95 N

Tension 1 = 2.95N

Tray	Wavelength /m	Frequency /Hz	Distance between the node/m
1	3.06	13.6	1.53
2	1.60	27.0	0.80
3	1.04	40.7	0.52
4	0.74	56.1	0.37
5	0.71	69.3	0.31
6	0.52	81.3	0.26
7	0.43	99.4	0.22

speed of wave v = sqrt( T/u ) = sqrt( 2.95 / 0.00117 ) = 50.02 m/s.



then we plot the frequency of the wave versus 1/wavelength in excel to get a graph:

the slope of the graph is 43.01 which very close to the speed of the wave v = 50.02 m/s.

for the second part of the experiment, we reduce the tension, we use 200 g = 0.2 kg, tension = 0.2 * 9.8 = 1.97 N

Tension 2 = 1.97 N

Tray	Wavelength /m	Frequency /Hz	Distance between the node/m
1	3.06	16.8	1.53
2	1.56	33.8	0.76
3	1.00	51.0	0.50
4	0.74	67.2	0.37
5	0.60	85.8	0.30
6	0.49	103.6	0.25
7	0.45	120.6	0.22

from equation wave speed v = sqrt( T / u ) = sqrt( 2.97 / 0.00117 ) = 50.38 m/s

we plot the frequency ofthe wave versus 1/wavelength to get a graph:

we get the slope is 52.043 which is very close to the wave speed we get from equation above.

ratios of wave speeds for case 1 compared to 2(experiment wave speeds) = 43.01/52.04 = 0.83.

ratios of wave speeds for case 1 compared to 2( predicted wave speeds) = 50.02 / 50.38 = 0.99.

the two ratios are close, but not the same.

the measured frequencies for case 1 equal to nf1, where n is the number of the harmonic

27/13.6~2

40.7/13.6~3

56.1/13.6~4

69.3/13.6~5

81.3/13.6~6

99.4/13.6~7

the ratio of the frequency of the second harmoic for case 1 compared to case 2.

16.8 / 13.6 = 1.24

33.8/27=1.35

51/40.7=1.25

67.2/56.1=1.20

85.8/69.3=1.25

103.6/81.3=1.27

120.6/99.4=1.21

we take look at all the data of the ratio of the frequency of the second harmonic for case 1 compared to case 2, all the ratio are closed to 1.25, the reason have these variable ratio because the when we do the experiment, we have so many error percent, so make the data are not 100% acurate.

Conclusion:

from this experiment, we get that when the length of the string and the tension of the string is stable, the wavelength will decrease by the frequency increase. and the speed of the wavelength is independent of the frequency is only depend on the tension and the linear density of the string. after the experiment, we do the data analyze, and calculate all he ratio requirement by the experiment. and measured frequencies for case 1 is mostly equal to nf1, and the ratio of the wave speeds for case 1 compared to 2 is mostly equal to the ratios of the predicted wave speeds. but our experiment have error such as we measure the lenght of the string, or determine the perfectly wavelenght frequency is not exact. but overall our experiment make sense.