In: Physics
Using detailed incident angle and refracted angle measurement data. Determine the refractive index of each material and compare with the theoretical values.
Data group 1 Theoretical index: 1.33 incident angle: 10, 20, 30, 40, 50, 60, 70, 80 refracted angle: 7.2, 14.63, 22.03, 28.92, 35.9, 40.67, 44.12, 48.72
Data groups 2 Theoretical index: 1.45 incident angle: 10, 20, 30, 40, 50, 60, 70, 80 refracted angle: 6.86, 13.74, 19.65, 25.72, 32.5, 35.59, 42.16, 42.65
Data group 3 Theoretical index: 1.22 incident angle: 10, 20, 30, 40, 50, 60, 70, 80 refracted angle: 7.84, 15.66, 25.12, 32, 37.56, 43.77, 50.18, 52.18
Data Goup 1
Given that the theoritical index value , = 1.33
We know that according to Snell's law the refrective index is,
,
( where , i = incident angle and r = refracted angle)
Now, we can calculate the refrective index by Snell's law by Using given experiment data ( Groop 1)
In same way calculated index value is provided in Bellow table
Table 1(for Group 1 data)
Incident angle,i | refracted angle, r | refrective index, |
10 | 7.2 | 1.38 |
20 | 14.63 | 1.35 |
30 | 22.03 | 1.33 |
40 | 28.92 | 1.32 |
50 | 35.9 | 1.30 |
60 | 40.67 | 1.32 |
70 | 44.12 | 1.34 |
80 | 48.72 | 1.31 |
For Group 1 data the average refrective index
(1.38 +1.35 +1.33+1.32+1.30+1.32+1.34+1.31)/8
= 1.33
So, the theorical and experimental average vale of refrective index are same.
For Group 2 data
Ginen that theoritical refrective index = 1.45
Table 2 for Group 2 data
Incident angle,i | refracted angle,r | refrective index, |
10 | 6.86 | 1.45 |
20 | 13.74 | 1.43 |
30 | 19.65 | 1.48 |
40 | 25.72 | 1.48 |
50 | 32.5 | 1.42 |
60 | 35.59 | 1.48 |
70 | 42.16 | 1.40 |
80 | 42.65 | 1.45 |
For Group 2 data, the average refrective index value,
=
1.45+1.43+1.48+1.48+1.42+1.48+1.40+1.45/8
= 1.44
So, (1.45-1.44) = 0.01 difference between experiment value of refrective index .
For Group 3 data
Theoritical refrective index is = 1.22
For Group 3 data the experiment value of index is given in table 3:
Table 3:
Incident angle,i | refracted angle,r | refrective index, |
10 | 7.84 | 1.27 |
20 | 15.66 | 1.26 |
30 | 25.12 | 1.17 |
40 | 32 | 1.21 |
50 | 37.56 | 1.25 |
60 | 43.77 | 1.25 |
70 | 50.18 | 1.22 |
80 | 52.18 | 1.24 |
The average experiment value of refrective index is =
1.27+1.26+1.17+1.21+1.25+1.25+1.22+1.24/8
= 1.24
So, (1.22-1.23)= - 0.01
There is 0.01 difference in theoritical and experiment value of refrective index.