To Determine the Angle of Minimum Deviation for a Given Prism

Objective:

To determine the angle of minimum deviation (d_m or D_m) for a glass prism by plotting a graph, (prism i- d graph) between the angle of incidence (∠i) and the angle of deviation (∠d).

Apparatus Required:

Glass prism (50 x 50 mm)

Drawing board (wooden)

Board pins

Drawing push pins (optical pins)

White sheet of paper

Protractor

Pencil

Ruler

Angle of minimum deviation – Image

Theory: Refraction Through a Prism

The reason for refraction of light is because of the adjustment (change) of speed of light starting with one medium then on to next.

At the point when the beam of light goes from rarer to denser, the angle of incidence is more predominant (greater) than that of the angle of refraction. The refracted beam twists (bends) towards the normal.

At the point when the beam of light goes from denser to rarer, angle of incidence is less than the angle of refraction.  The refracted beam twists (bends) away from the normal.

When a ray of passes through a prism, it undergoes refraction twice. Once at each refracting surface and deviates from its original path. The angle of deviation (∠d) is angle between the incident ray and the emergent ray.

The deviation depends on, the angle of incidence (∠i). the angle of the prism (∠A), the refractive index (µ) of the material of the prism.

At the angle of minimum deviation, the ray passes through the prism symmetrically, such that

∠i = ∠e and the refraction at both faces are equal, ∠r₁=∠r₂=∠r

Procedure: First method

White sheet of paper is fixed on a drawing board.

Place the glass prism on the white sheet and trace the outline of the prism, mark it as ABC.

Draw a normal NN’ at point Q on one face AB.

Draw incident rays at different angles (e.g., 30⁰  35⁰ 40⁰ 45⁰ 50⁰ 55⁰ 60⁰) using a protractor. Angle of incidence is the angle between incident ray and the normal.

Now fix two pins (P₁ and P₂) along the incident ray. View the pins through the prism from other side (AC) and fix two more pins (P₃ and P₄) such that they appear in line with P₁ and P₂.

Now measure the angle of deviation (∠d) with the help of a protractor, which is the angle between the incident ray and the emergent ray.

Perform the experiment for at least 5 to 6 different angles of incidence.

Plot a graph with angle of incidence (∠i) on X-axis and the angle of deviation (∠d) on the Y-axis.

The prism and curve will show a minimum point, which corresponds to the angle of minimum deviation (d_m or D_m).

Second Method: (Refer the image)

XX’ is a straight line drawn parallel to the length of the paper, make sure that it is in the center of the paper.

Place the prism with its refracting face AB on the line XX’.

Mark the boundary of the prism.

Draw normal to the side AB of the prism.

Keep the angle of incidence as (e.g., 30⁰  35⁰ 40⁰ 45⁰ 50⁰ 55⁰ 60⁰) using a protractor.

Now fix two pins (P₁ and P₂) along the incident ray. View the pins through the prism from other side (BC) and fix two more pins (P₃ and P₄) such that they appear in line with P₁ and P₂.

Now measure the angle of deviation (∠d) with the help of a protractor, which is the angle between the incident ray and the emergent ray.

Perform the experiment for at least 5 to 6 different angles of incidence.

Angle of Minimum Deviation- Observations

Angle of minimum deviation-Graph

Result:

The angle of deviation for the given prism is found to be 37⁰ (From the graph)

Viva voce Questions:

1. What is a prism?
2. What is meant by the angle of deviation?
3. What is the angle of minimum deviation
4. What is the condition for minimum deviation in a prism?
5. How does the angle of deviation vary with the angle of incidence?
6. What is the relationship between the refractive index (n), the angle of prism (A), and the angle of minimum deviation (D_m)?
7. How does the colour (wavelength) of light affect the angle of minimum deviation?
8. What is meant by dispersion of light?
9. Why does a glass slab not produce spectrum like a prism?
10. Why are there two angles of incidence for the same value of deviation (except at minimum deviation)
11. What is the significance of plotting a graph between angle of incidence and angle of deviation?
12. What precautions should be taken during the experiment?
13. What is VIBGYOR?
14. What is the refracting angle of a prism?
15. How many edges does a triangular prism have?
16. What is the importance of the minimum deviation position in practical measurements?
17. How does immersing a prism in a liquid of higher refractive index affect the angle of minimum deviation?
18. Which colour deviates most and least in a prism?
19. What is the formula for refractive index using minimum deviation and prism angle?
20. What happens to the emergent ray at the position of minimum deviation?

 

Answers:

1. Prism is a homogeneous, transparent optical device with at least two non-parallel, flat, polished surfaces inclined at an angle, used to refract light.
2. Angle through which a light ray is turned from its original path as passes through a prism.
3. The smallest value of the angle of deviation observed when the angle of incidence varied. At this point the refracted ray is exactly parallel to the base of the prism.
4. At minimum deviation, the angle of incidence equals the angle of emergence and the refracted ray inside the prism is parallel to its base.
5. As the angle of incidence increases the angle of deviation first decreases, reaches a minimum value and then increases again.
6. n =sin (A+Dm/2)/sinA/2
7. Angle of minimum deviation varies for different colours. It is larger for violet and smaller for red due to their different refractive indices.
8. The phenomenon of white light splits onto its constituent colours (VIBGYOR)when passing through a prism
9. Glass slab has parallel surfaces, so the deviations produced at entry and exit cancel each other resulting in no dispersion.
10. For a given deviation (other than the minimum deviation), two different angles of incidence can produce the same deviation due to the symmetry of the deviation curve.
11. The graph helps in visually identifying the angle of minimum deviation as the lowest point and demonstrates the relationship between the two angles.
12. Fix the prism firmly | Use sharp pins and mark their positions accurately | Avoid disturbing the setup while taking readings | Draw a smooth curve for the graph.
13. VIBGYOR is an acronym for the sequence of colours in the visible spectrum. Violet, Indigo, Blue, Green, Yellow, Orange and Red.
14. It is the angle between the two plane surfaces of the prism through which light enters and emerges.
15. A triangular prism has nine edges.
16. At minimum deviation, the measurement is most accurate as the path of the light is symmetric, reducing errors in calculation of refractive index.
17. The angle of minimum deviation decreases with a refractive index closer to that of the prism material.
18. Violet deviates the most and red deviates the least due to their respective refractive indices.
19. n =sin (A+Dm/2)/sinA/2
20. At minimum deviation, the emergent ray is far from the incident ray as possible, and the path inside the prism is parallel to the base.

Links to this experiment:

Experiment: To Determine the Focal Length of a Convex lens by Plotting Graphs Between u and v and 1/u and 1/v

Experiment: To Determine the Resistivity of Two/Three Wires by plotting a Graph of Potential Difference (V) vs Current (I)