To Determine Angle of minimum Deviation for a given Prism by Plotting a Graph between Angle of Incidence & the Angle of Deviation

Aim/Aim of Experiment

To determine Angle of minimum deviation for a given Prism by plotting a graph between Angle of incidence and the Angle of deviation.

Apparatus/Material Required

• A Drawing board
• A Prism
• A white sheet of paper
• Drawing pins
• A Pencil
• A half meter scale
• Graph Paper
• Office pins
• A Protractor.

Theory

• Angle of Prism – The angle between the two refractive surfaces is called angle of prism.
• Angle of Deviation – The angle through which a ray of light turn away from its original path on passing through a prism, is called angle of deviation.
• Angle of minimum Deviation – The least value of angle of deviation is known as angle of minimum deviation.

The refractive index (n) of the material of the prism is given by:

n=sin[(A+D_m)/2]/sin(A/2),

where A is angle of the prism and D_m is the minimum deviation.

Ray Diagram

Procedure

1. Take & place the white sheet of paper and fix it on drawing board with the help of drawing pins.
2. Draw a straight line XX’ parallel to the length of the paper nearly in the middle of the paper.
3. Mark the there points Q1, Q2 and Q3 at suitable distances on the straight line XX’.
4. Draw normals N1Q1, N2Q2, N3Q3 on these three points Q1, Q2, Q3 as shown in ray diagram.
5. Draw straight lines R1Q1, R2Q2, R3Q3 making angles of 35°, 40°, 45° and so on, with the normal drawn at each of these points.
6. Measure the prism angle A is with the help of protector and note it.
7. Mark one coner of the prism as A and take it as the edge of the prism for all the
   observations.
8. Put the prism with its refracting face AB in the line XX’ and point Q1 in the middle of AB, then mark the boundary of the prism.
9. Fix two or more office pins P1 and P2 vertically on the line R1Q1 making angle 35° with the normal. The distance between the pins should be 10 mm or more.
10. Look the images of point P1 and P2 through face AC and close your left eye and bring open right eye in line with the two images.
11. Fix two office pins P3 and P4 vertically and 10 cm apart such that the open right eye sees pins P4 and P3 and images of P2 and P1 in one straight lines.
12. Now remove pins P3 and P4 and encircle their pricks on the paper.
13. Repeat the same steps of procedure 8 to 12 with points Q2 and Q3 for i = 40° and 60° respectively.

To Measure D in different cases:

1. Draw straight lines through points P4 and P3 (pin pricks) to obtain emergent rays T1, S2T2, S3T3 and so on.
2. Then produce T1S1, T2S2, T3S3 inward in the boundary of the prism to meet produced incident rays R1Q1, R2Q2, R3Q3 at points F1, F2, and F3.
3. Now measure angles K1F1S1, K2F2S2 and K3F3S3 these gives angle of deviation D1,D2 and D3 then note values of these angles on the paper.

To Measure A

1. Measure angle BAC in the boundary of the prism, this gives angle A.
2. Record your observations.

Observations

• Angle of prism ‘A’ = 60°.

Sr. No.	Angle of incidence ∠i	Angle of deviation ∠D
1.	35°	51°
2.	40°	47°
3.	45°	44°
4.	50°	48°
5.	55°	53°

Calculations

Plot a graph between angle of incidence ∠i and angle of deviation ∠D by taking ∠i along X-axis and ∠D along Y-axis. From this graph, calculate the value of single of minimum deviation Dm corresponding to the lowest point of the graph.

Let the value of angle of minimum deviation = 38°.

Then, n=sin[(A+Dm)/2]/sin(A/2)

n = sin[(60+38)/2]/sin(60/2) = sin(49°)/sin(30°)

So, n = 1.5°.

Result

• The Angle of minimum Deviation, Dm = 38°.
• Refractive index of the material of the prism, n = 1.5°.
• Graph indicates that as the angle of incidence (∠i) increases, the angle of deviation (∠D) first decreases and attains a minimum value and then starts increasing for further increase in the angle of incidence.

Precautions

• A sharp pencil should be used to drawing the boundary of the prism.
• The angle of incidence should lie between 35° to 60°.
• The placement of the office pins should be vertical.
• The distance between office pins not be less then 10mm.
• Proper arrowhead should be drawn to indicate the incidence, refracted and the emergent ray.
• The angle of prism used should be the same for all the observations.

Sources of Error

• Pin pricks may be thick.
• Measurement of angles may be wrong.
• Using different angle of prism for all observations.

Viva Voice Questions with Answers

1. Define a prism.

Answer: A prism is a piece of a transparent material bounded by three rectangular surfaces forming a triangle.

2. Define edge of the prism.

Answer: One surface (which may be opaque or transparent) is called base. Other two surfaces of a Prism are transparent and are called refracting surfaces. The line along which the refracting surfaces meet, is called the edge of the prism.

3. Define angle of prism.

Answer: The angle between the two refracting surfaces, is called the angle of prism or refracting angle of prism.

4. Define angle of deviation.

Answer: The angle through which a ray of light turns away from its original path on passing through a prism, is called angle of deviation.

5. On what factors does the angle of deviation depend?

Answer: The angle of deviation depends upon the following factors :

1. The angle of incidence.
2. The refracting angle of the prism.
3. The material of the prism. (Refractive Index).
4. The colour of the light used i.e., wavelength of light.

6. Define angle of minimum deviation.

Answer: The least value of the angle of deviation is known as the angle of minimum deviation. It is represented by the symbol Dm.

7. What is the specialty about minimum deviation?

Answer: Under minimum deviation condition, light ray travels inside prism parallel to the base of the prism and the angle of incidence = angle of emergence.

8. Does the angle of minimum deviation depend upon the colour of light used?

Answer: Yes, it is different for different colours or wavelengths.

9. What word helps in remembering the name of seven colours into which white light is splitted?

Answer: The word is VIBGYOR.

10. What name is given to the phenomenon of splitting white light into seven colours?

Answer: The phenomenon is called dispersion of light.

11. What does the graph between i and D indicate?

Answer: There is only one unique value of angle of incidence for which the deviation is minimum.

12. Why there are two values of angle of incidence for one value of angle of deviation?

Answer: If the emergent ray be reversed, then angle e becomes i and angle i becomes e. The reversed ray will have same deviation as before.

13. Hence, i and e are two different values for same angle of deviation. Which colour will travel (i) fastest (ii) slowest in prism?

Answer: (i) Red colour (ii) Violet colour.

14. Does a beam of white light give a spectrum on passing a hollow prism?

Answer: No. Because dispersion does not occurs in air.

15. Which colour deviate (i) Most (ii) Least?

Answer: (i) Violet (ii) Red.

16. Will all colour of light travel with same speed inside a prism?

Answer: No. Red colour travel fastest and violet colour travel smallest.

17. Which colours have hightest and smallest refractive index? Why?

Answer: Refractive index is smallest for red colour and that is highest for violet colour.

Refractive index = 1/wavelength.

18. What is Cauchy relation?

Answer: It is the relation between refractive index of a transparent medium and colour of light.

Cauchy Relation, n=A+B/λ²+C/λ⁴ .

19. Can X-rays be dispersed?

Answer: Yes.

20. What is angular deviation?

Answer: The angle between the emergent rays of any two colours is called angular dispersion of those colours.

21. On what factors angular deviation depends?

Answer: (i) Angle of prism (ii) refractive index.

22. What is dispersive power of prism?

Answer: It is define as the ratio of the angular dispersion for these two colours to the mean deviation produced by the prism.

23. What is factor on which dispersive power depends?

Answer: It depends upon refractive index of the material of prism.

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