Question

In: Physics

Using detailed incident angle and refracted angle measurement data. Determine the refractive index of each material...

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

Solutions

Expert Solution

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.


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