To determine angle of minimum deviation for a given prism by plotting a graph between angle of incidence and angle of deviation

Aim

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

Materials Required

• A drawing board
• A white sheet of paper
• A prism
• Drawing pins
• Pencil
• A half-metre scale
• Office pins
• Protractor
• Graph paper

Theory

Refraction takes place when a light ray travels from one medium to another resulting in deviation of the emergent ray from that of the incident ray. Following is the refractive index of the material used in the prism:

(n=frac{sin(frac{A+D_{m}}{2})}{sin(frac{A}{2})})

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

Ray Diagram

Procedure

1. Place the white sheet of paper on the drawing board and fix it with the help of drawing pins.
2. XX’ is the straight line which is drawn parallel to the length of the paper such that it is in the middle of the paper.
3. Mark points Q₁, Q₂, Q₃…… on the straight line XX’ at a distance of 5 cm each.
4. N₁Q₁, N₂Q₂,… are the normals that are drawn on the points Q₁, Q₂,… as shown in the ray diagram.
5. Make angles of 35°, 40°,….,60° by drawing straight lines R₁Q₁, R₂Q₂,…….. With respect to the normals.
6. To take one edge of the prism for all the observation, mark any corner of the prism as A.
7. Place the prism with its refracting face AB on the line XX’ and on the point Q₁ and also in the middle of AB.
8. Mark the boundary of the prism.
9. On the line, R₁Q₁, fix office pins vertically and mark them as P₁ and P₂. the distance between these pins should not be less than 10mm.
10. Through prism face, AC, look for the images of the points P₁ and P₂.
11. Close your left eye and with the right eye open, bring it in line with the two images.
12. Fix the other two office pins vertically and name them as P₃ and P₄. These pins should be 10cm apart from each other. P₃ and P₄ should be in one straight with respect to the images of P₁ and P₂.
13. Encircle the pricks of pins P₃ and P₄.
14. For points, Q₂, Q₃,…. for angle 40°, 45°,…..60°, repeat the steps 7 to 13.

To measure D in a different case

1. To get emergent rays S₁T₁, S₂T₂,….. draw straight lines through P₄ and P₅.
2. Inward the boundary of the prism to produce T₁S₁, T₂,S₂….. so that they meet incident rays R₁Q₁, R₂Q₂,…. at points F₁, F₂,…
3. To obtain the angle of deviation D₁, D₂,…. measure the angles K₁F₁S₁, K₂F₂,S₂,…….
4. Note these angles.

To measure angle A

1. To get angle A, measure the angle BAC in the boundary of the prism.
2. Record the observations.

Observations

The angle of prism, A =……

Calculations

To plot the graph between the angle of incidence ∠i and the angle of deviation ∠D, take ∠i along the x-axis and ∠D along the y-axis. Minimum deviation D_m can be found from the graph which would be corresponding to the lowest point in the graph.

Let the value of angle of minimum deviation, D_m = …..

Then, (n=frac{sin(frac{A+D_{m}}{2})}{sin(frac{A}{2})})

Result

• The angle of minimum deviation, D_m = ………
• Refractive index of the material of the prism, n = ……
• The graph indicates that the angle of incidence increases, the angle of deviation first decreases to attain the minimum value of D_m and then increases as the angle of incidence increases.

Precautions

• 35°-60° is the angle of incidence that needs to be maintained.
• The placement of the pins must be vertical.
• The placement of two pins should be such that the distance is not more than 10mm.
• To represent incident and emergent rays arrowheads must be marked.
• The angle of prism used should be the same for all the observations.

Sources of Error

• The pricks made by the pins might be thick.
• Angles might go wrong while measuring them.

Viva Voice

Q1. Name the factors on which the angle of deviation depend on.

Ans: Following are the factors on which the angle of deviation depend on:

• The angle of incidence
• The refracting angle of the prism
• Refractive index of the material used in the prism
• The wavelength of the light ray

Q2. Define angular deviation.

Ans: Angular deviation is defined as the ratio of the angular dispersion of the two colours to produce the deviation by the prism.

Q3. Name the factor on which dispersive power depends.

Ans: Dispersive power depends on the refractive index of the material used in the prism.

Q4. Name the colours with the highest and smallest refractive index.

Ans: Violet colour has the highest refractive index while the red colour has the smallest refractive index.

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