Student Name: Fumiya Shigematsu Partner’s name(s): write lab partners names here

Snell’s Law Lab

Data Collection

This is the setup that was used during the experiment.

Table1: This table is the values for incident and refracted angle, which were manipulated several times

and it is divided into two sections, which are the raw data and processed data.

Incident Angle /±𝟎. 𝟓° Refracted Angle ±𝟎. 𝟓° Sin(Incident Angle)

/±𝟎. 𝟎𝟏°

Sin(Refracted Angle)

/±𝟎. 𝟎𝟏°

11.5 6.0 0.20 0.10

15.0 10.0 0.26 0.17

18.5 18.5 0.32 0.20

21.5 15.5 0.37 0.27

28.0 20.0 0.47 0.34

32.0 21.0 0.53 0.36

34.0 28.0 0.56 0.47

35.5 28.5 0.58 0.48

40.0 32.5 0.64 0.54

45.0 40.5 0.71 0.65

48.5 42.0 0.75 0.67

55.0 53.0 0.82 0.79

※Angles indicated in the table are measured by a protractor.

θ1

glass θ2

Glass (n1)

Air (n2)

Laser

pointer

θ1

Student Name: Fumiya Shigematsu Partner’s name(s): write lab partners names here

Snell’s Law Lab

Data Analysis and Processing

Equation of this graph: y = 1.083x − 0.1403

From the graph above, it can be said that there is a linear relationship between Sin (incident angle) and

Sin (refracted angle). Thus, it verifies the Snell’s Law.

n1sinθ1 = n2sinθ2

The index of refraction for n2, air is approximately 1 (1.00029) because the result will not be precise

enough to see difference due to the equipment used to measure the angle. Additionally, the value for n1

can be interpreted from the graph, which is the slope, 1.08

※ Found the value for air from Internet: http://hypertextbook.com/facts/2005/MayaBarsky.shtml

Calculating Critical Angle

In order to calculate the critical angle for a light ray exiting glass, the angle of the refracted light ray θ2is

set to 90°. Using Snell’s Law:

n1sinθ1 = n2sinθ2

sinθ1 =n2sinθ2

n1

=1sin (90)

1.08

sin−10.9259 = 67.8°

Student Name: Fumiya Shigematsu Partner’s name(s): write lab partners names here

Snell’s Law Lab

Sample Calculation

% error calculation of the data collection

% 𝐸𝑟𝑟𝑜𝑟 =|Actual − Experimental|

Actual× 100

= (1.5 − 1.08)

1.5 × 100

≅ 28%

※ The actual index of refraction of glass is gained from the internet:

http://mintaka.sdsu.edu/GF/explain/optics/refr.html

Uncertainty for the Critical Angle

Uθ1 = θ1 ×Uθ2

θ2

= 67.8 ×0.01

90

≅ 0.1°

Uncertainty for the Sin (Incident)

Ui = Sin(incident) ×Ui

i

= 0.20 ×0.5

11.5

≅ 0.01°

Uncertainty for the Sin (Refracted)

Ur = Sin(refracted) ×Ur

r

= 0.10 ×0.5

6.0

≅ 0.01°