Refractive Index Determination: Glass Slab and Prism Experiments
Experiment 6: Refractive Index Determination
Part 1: Refractive Index of a Glass Slab (Pin Method)
Aim
To determine the refractive index of a glass slab material using the pin method.
Apparatus and Materials
Glass slab, drawing board, drawing pins, hairpins, paper, scale, and protractor.
Theory
The refractive index, n, of glass with respect to air is defined by Snell’s Law:
n = sin i / sin r
where i is the angle of incidence and r is the angle of refraction.
A graph plotted with sin r along the X-axis and sin i along the Y-axis will be a straight line passing through the origin. The slope of this graph gives the value of n.
Experimental Data (Glass Slab)
| No. of Obs. | ∠i | sin i | ∠r | sin r | n (from graph) |
|---|---|---|---|---|---|
| 1 | 15° | 0.25 | 10° | 0.17 | |
| 2 | 25° | 0.42 | 16° | 0.28 | |
| 3 | 35° | 0.58 | 22° | 0.37 | 1.5 |
| 4 | 20° | 0.34 | 13° | 0.22 | |
| 5 | 30° | 0.50 | 20° | 0.34 | |
| 6 | 40° | 0.64 | 26° | 0.44 |
Plotting of Graph
Taking the length of … divisions = units, sin r is plotted along the X-axis and sin i is plotted along the Y-axis. The graph is a straight line passing through the origin. The slope of the graph is determined.
Result (Glass Slab)
Refractive index of glass n = sin i/sinr
= Slope of the graph = PQ/ PR = 1.5
Precautions (Glass Slab)
- The difference in angles of incidence should not be less than 5°.
- Pins should be fixed exactly vertical.
Part 2: Refractive Index of a Prism (Minimum Deviation)
Aim
To determine the angle of minimum deviation for a given prism by plotting a graph between the angle of incidence (I) and the angle of deviation (D), and subsequently calculate the refractive index of the prism material.
Apparatus and Materials
Prism, drawing board, paper, drawing pins, hairpins, and protractor.
Theory
The angle of deviation (D) is related to the angle of incidence (I) and the prism angle (A) by the relation:
D = I + I‘ – A, where I‘ is the angle of emergence.
The refractive index (n) of the material of the prism for a specific color of light is given by:
n = {sin((A+Dm)/2)} / {sin (A/2)}
Where A is the angle of the prism and Dm is the angle of minimum deviation (determined from the I-D graph).
Experimental Data (Prism)
1) Table for angles I and D:
| No. of Obs. | I (°) | D (°) |
|---|---|---|
| 1 | 35 | 45 |
| 2 | 40 | 42 |
| 3 | 45 | 40 |
| 4 | 50 | 38 |
| 5 | 55 | 40 |
| 6 | 60 | 43 |
2) Angle of the prism A:
A = (60° + 60° + 60°)/3 = 60°
3) Plotting of I-D graph:
Angle I is plotted along the X-axis and angle D along the Y-axis for the recorded values. The graph is a curve. The angle of minimum deviation Dm is determined from the lowest point on the graph.
Calculation
The values of A and Dm are substituted into the formula to calculate n.
n = 1.5
Result (Prism)
- The angle of deviation D first decreases with the increase in the angle of incidence, attains a minimum value (Dm), and then increases with further increase in the angle of incidence, as indicated by the I-D curve.
- The Refractive Index of the prism material, n = 1.5.
Precautions
- The same angle of the prism should be used for all observations.
- Proper arrows should be drawn to indicate the direction of the rays.
Sources of Error
- Measurement of angles may not be accurate.
- Pin pricks may be thick.
