Data Sheet MEASUREMENT  OF THE INDEX OF REFRACTION OF WATER. 

Blank Data Sheet here 
FOR THE INDEX OF REFRACTION LAB, your INTRO/ABSTRACT  should state what the purpose of the  experiment was. I think you know what it is. To measure *something* using a tank of shallow water and two slots. (Include a diagram with key geometry.) What is that "something?" Just state in your abstract/intro whether or not you successfully completed the goal  by quoting your percent error and whether or not nw = nacc = 1.33 falls within the range I wrote on the board. You should compute the percent error as well as range information  discussed  next: 

| nbest - nacc  | < overall error

nacc = 1.33

(Overall error)2 = a2 + b2.

Take the square root of both sides to be get overall error.

Here, 

a = [cos (theta_fbest ) /sin(theta_ibest)]*
Δtheta_f
b =  [sin (theta_fbest ) *csc(theta_ibest)*
cot(theta_ibest)* Δtheta_i
[REMEMBER TO CONVERT TO RADIANS IF THE FINAL  OR INITIAL ANGLE CHANGE Δtheta IS USED OUTSIDE THE ARGUMENT OF THE SINE OR COSINE FUNCTION.]
These expresions are obtained by taking partial derivatives as shown in class.

Remember,

theta_fbest and theta_ibest  are each the average of 4 measurements; see data sheet below.

In one case,  error =  lc/4 = 0.25/4 = 0.0625 = 0.06.
Typical numbers might be : 50.375 (before rounding to 4 sig fig.),
50.125 (before rounding to 4 sig fig.),  or 50.00

In another case,  lc/2 = 0.125 = 0.1. Then you might have collected numbers like:

50.25   or 50.00.

Include the data sheet and all calculations with the report. Sample data is included in the table below.  Note only certain values of numbers are allowed given Least Count (LC) rules. You are doing a   "full" report, including all the sections stated at this site:
http://www.nvaphysics.com/2A_au08/labs/physics_lab_report_formats.htm
Explore the entire, included  site at
http://www.physics.upenn.edu/~uglabs/
for tips on sig. figs. and other topics of interest.

 

 

 

LC/2 = 0.25/2 = 0.125 = 0.1

 

theta_i

 

 

35.50
35.75
35.50
35.50

theta_ibest    (average of the 4 above)

Δtheta_iinst  = 0.125 = 0.1

(theta_imax theta_imin)/4 =

Δtheta_i (larger of previous two.)


theta_f

52.25

 

52.00
52.00
52.25

theta_fbest (average of the 4 above)

Δtheta_finst  =0.125 = 0.1

(theta_fmax theta_fmin)/4

Δtheta_f (larger of previous two.)

 

nbest

  sin(theta_fbest) /sin (theta_ibest) =

 

See formula at the top of the page  overall error in nbest  
  Percent error  
  Compare:  
| nbest -nacc | < overall error in nbest