PHYSICS LAB REPORT – JIDAPAS AN-ADIREKKUN (MY)
PHYSICS LAB REPORT – CALCULATING THE REFRACTIVE INDEX OF A GLASS Data Processing and Processing Data Collection Incident Refracted Angle (r°) (±1°) Angle (i°) Trial1 Trial2 Trial3 Trial4 Trial5 ( 15 10 10 11 11 10 30 22 20 20 21 20 45 30 29 28 29 28 60 36 37 36 35 37 75 43 43 43 41 42 Table1: The incident angles and the refracted angles taken from 5 trials of experiment The column labeled ‘Incident angle’ contains 5 different angles of incidence measured in degrees (°). They are the angles between the light rays from the ray box that struck the glass block and the normal which is an imaginary line parallel to the surface of the glass block. These angles were measured using a protractor which had the least reading equaled to 1°. However, since the rays had a considerable thickness, the uncertainties of the incident angles were taken to be 1°. The column labeled ‘Refracted angle’ contains the angles of refraction (r), measured in degrees (°), of the light rays after being refracted by a glass block. The refracted rays were obtained by joining the point where the incident rays entered the glass block and the point where the emergent rays left the block. The angles between the refracted rays and the normal were then measured using a protractor which had the least reading equaled to 1° to obtain the refracted angles, which were recorded to 2 significant figures. Five trials of the experiment were performed to reduce the effect of random errors. Due to the considerable thickness of the light rays, the uncertainties of the refracted angles were taken to be 1°.
Data Processing Sin i (°) 0.26 0.02 0.50 0.02 0.71 0.01
Trial1 0.17
Trial2 0.17
Sin r (°) Trial3 Trial4 0.19 0.19
0.37
0.34
0.34
0.36
0.34
0.50
0.48
0.47
0.48
0.47
Trial5 0.17
Average 0.18 0.01 0.35 0.02 0.48 0.02
PHYSICS LAB REPORT – JIDAPAS AN-ADIREKKUN (MY) 0.59 0.60 0.59 0.57 0.60 0.87 0.01 0.68 0.68 0.68 0.66 0.67 0.97 0.01 Table2: The sines of the incident angles and the refracted angles
0.59 0.02 0.67 0.01
The column labeled ‘Sin I’ contains the sines of the incident angles in degrees. (Sin i) were calculated by the formula: sin i = sin(incident angle), and were recorded corrected to 2 s.f. For i = 15°: sin i = sin(15°) = 0.26 (2 s.f.) For i = 30°: sin i = sin(30°) = 0.50 (2 s.f.) For i = 45°: sin i = sin(45°) = 0.71 (2 s.f.) For i = 60°: sin i = sin(60°) = 0.87 (2 s.f.) For i = 75°: sin i = sin(75°) = 0.97 (2 s.f.) Then the incident angles were converted from degree into radians:
angle∈radians=angle∈degree ×
For i = 15°:
15 ×
π 180
π π = 180 12
The uncertainties the incident angles were calculated by using a formula 1
|dθd sin θ|∙ ∆ θ
∆ sin θ=
For i = 15°:
For i = 30°:
For i = 45°:
For i = 60°:
For i = 45°:
¿|cos θ|∙ ∆ θ
where
| 12π |∙ 180π =0.02 π π ∆ sin θ=|cos |∙ =0.02 6 180 π π ∆ sin θ=|cos |∙ =0.0 4 180 π π ∆ sin θ=|cos |∙ =0.0 3 180 5π π ∆ sin θ=|cos |∙ =0. 0 12 180 ∆ sin θ= cos
∆ sin θ
is the uncertainty of
sin θ
(2 s.f.)
(2 s.f.)
1 (2 s.f.)
1 (2 s.f.)
045 = 0.00 (2 s.f.)but since its
uncertainty is not 0, it is taken to be 0.01 1Uncertainties & Error Analysis Tutorial http://physics.wustl.edu/introphys/Phys117_118/Lab_Manual/Tutorials/ErrorAnalysisTutorial.pdf (accessed on 2nd September 2012)
PHYSICS LAB REPORT – JIDAPAS AN-ADIREKKUN (MY) The column labeled ‘Sin r’ contains sines of the refracted angles in degrees. (Sin r) were calculated by the formula: sin r = sin(refracted angle), and were recorded corrected to 2 s.f. Trial1: For r = 10°: sin r = sin(10°) = 0.17 (2 s.f.) For r = 22°: sin r = sin(22°) = 0.37 (2 s.f.) For r = 30°: sin r = sin(30°) = 0.50 (2 s.f.) For r = 36°: sin r = sin(36°) = 0.59 (2 s.f.) For r = 43°: sin r = sin(43°) = 0.68 (2 s.f.) The average values of sin r were calculated by:
average=
Trial 1+Trial 2+Trial 3+Trial 4+ Trial 5 ; 5
Where Trial1, Trial2, Trial3, Trial4, Trial5 are the sin r of that trials. For sin i = 0.26; average of sin r =
0.17+0.17+0.19+ 0.19+0.17 =0.18 ( 2 s . f . ) 5
For sin i = 0.50; average of sin r =
0.37+0.34+ 0.34+0.36+ 0.34 =0.35 ( 2 s . f . ) 5
The uncertainties of the average of sin r were calculated from the range of sin r of the 5 trials:
Range=
maximum value−minimum value 2
For sin i = 0.26:
Range=
0.19−0.17 =0.01 2
Data Presentation 0.80
f(x) = 1.96x 2.13x - 0.32 0.38
0.70 0.67 f(x) = 0.69x + 0 0.60
0.59
0.50
Average
0.48
Linear (Average) Linear (Average)
0.40
Minimum gradient Linear (Minimum gradient)
0.35
Maximum gradient
0.30
0.20
Linear (Maximum gradient)
0.18
0.10
0.00 0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
In Graph1, sine of incident angles (sin i) is plotted on the x-axis against the sine of refracted angles (sin r) (on the y-axis). The values are taken from Table2 and shown as blue data points. The vertical error bars are the uncertainty of the sin r and taken from the same table. The horizontal error bars shows the uncertainties of sin i, and are taken from Table2. The maximum gradient line is drawn by joining the negative vertical error bar of sin i = 0.26 and the positive vertical error bar of sin i = 0.97. The minimum gradient line is drawn by joining the positive vertical error bar of sin i = 0.26 and the negative vertical error bar of sin i = 0.97. The equations of the lines of best fit are generated automatically by Microsoft Excel, where the coefficients of ‘x’ represent the gradients of the lines.
Calculation to determine the refractive index of a glass block ‘n’ The formula used to calculate the refractive index of a glass block when the light rays travels from air to glass block is
sin i n glass = sinr nair ; where sin i is the incident angle, sin r is
the refracted angle, nglass is the refractive index of the glass block, nair is the refractive index of air. By manipulating the formula into the form
sinr nair = sin i n glass ; it can be seen that
represents the gradients (m) of the graph. Since nair is taken to be 1,
In this way, the refractive index of a glass block can be calculated by
m=
nair nglass
1 nglass
n glass=
1 m
For the average sin r: m = 0.6862 (shown as black colour in the graph)
n glass=
1 =1.46 (3 s.f.) 0.6862
For the minimum gradient line: m = 0.6699 (shown as red colour in the graph)
n glass=
1 0.6699
= 1.49 (3 s.f.)
For the maximum gradient line: m = 0.7265 (shown as green colour in the graph)
n glass=
1 =1.38 (3 s.f.) 0.7508
Uncertainties of the refractive index of the glass ± ∆ n glass=±
max n glass – min n glass 1.49−1.38 =± =± 0.06 2 2
Percentage error of the experiment The theoretical value of the refractive index ‘n’ of a Perspex glass is 1.4914 at 587.6 nm.2 The experimental value is
Percentage error=
Percentage error=
1.46 ±0.06
|Theoritical value−Experimental value| Theoritical value
|1.49−1.46| 1.49
× 100 =2.01
×100
(3 s.f.)
The theoretical value of ‘n’ does fall into the range of the experimental value after the uncertainties of ±0.06 has been allowed for. Also, the percentage error of this experiment is quite small. Thus, it can be concluded that experiment was precise and accurate.
2 Poly(methyl methacrylate) http://en.wikipedia.org/wiki/Poly(methyl_methacrylate)#Properties (accessed on 3rd September 2012)
Conclusion and Evaluation Concluding The refractive index of the glass block (n glass) was found from the graph of sin i plotted against sin r from experiment to be 1.46 0.06. The experiment was considered to be precise as the uncertainty of nglass is quite small, and accurate since after the uncertainties of 0.06 has been allowed for, the values of n glass does fall into the range of the theoretical value of 1.4914 (at 587.6 nm). Moreover, after allowed for the uncertainties, the average values lie on the straight line with the slope equals to
1 nglass
. However, it is possible that the difference between the theoretical value and
the experimental value is because the light source is not monochromatic, and the light rays would contain light with wavelengths different from 587.6 nm. And since the refractive index of Perspex glass depends to some extent on the wavelength of the light used3, the different wavelengths of the light would give different refractive index. In this experiment, the uncertainties of the values came from the random error caused by uncertainties in the position of the incident, refracted and the emergent rays, caused by the thickness and the scatterings of the light rays. And due to these uncertainties, the value of the incident and refracted angles contain some uncertainties too.
Evaluating Procedures
The procedures followed allow adequate data to be collected in order to successfully determine the refractive index of a glass block using Snell’s Law. And the data collected was good enough to give results with high precision and accuracy. The equipments used were good enough for the data needed to collect. However, the light rays emitted from the ray box had a considerable thickness, especially the emergent rays, thus the precise position of the emergent rays and the refracted rays could not be determined. Therefore the uncertainties of the refracted angles were increased. These uncertainties were considerably significant and accounted for the reduced precision and accuracy of the measurements the most.
3 http://www.filmetrics.com/refractive-index-database/Acrylic/Acrylate-Lucite-Plexiglass
The pencil lines drawn to show the position of the emergent rays also had a considerable thickness, and therefore the accuracy of position of the refracted rays and the refracted angles were reduced while the uncertainties increased. However, this was not the major factor affecting the reliability of the data. Much time was consumed in drawing the glass block, incident and refracted rays, and measuring the incident and refracted angles.
Improving the Investigation
A convex lens could be used to focus the light coming out from the light box to give less scattered and thinner rays with higher intensity. Also, a narrower slit could be used to narrow the light coming out from the light box. Moreover, more care should be taken to place the middle of the incident rays on the line drawn to indicate the incident rays, and to draw the emergent rays at the middle of the emergent rays. A mechanical pencil which produces narrower lines or a well-sharpened pencil could be used to draw the rays and glass block on the papers. The drawing of the blocks, the incident rays, and the normal at the point where the incident rays enter the glass block could be photocopied so that it would not be necessary to draw the same thing for all the five trials, and thus much time could be saved. The experiment should be conducted in the darker room so that the position of the light rays could be identified and draw more easily.
