Experiment to Determine the Angle of Minimum Deviation of a Glass Prism Using the i-D Graph

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

When a ray of light passes through a transparent glass prism, it undergoes refraction at both refracting surfaces. The ray bends towards the normal when it enters the prism from air and away from the normal when it emerges from the prism into air. As a result, the emergent ray is deviated from its original direction.

1. Angle of Deviation

The angle between the direction of the incident ray produced forward and the emergent ray is called the angle of deviation (D).

For a prism, the angle of deviation is given by:

D = i + e − A

where:

• i = Angle of incidence

• e = Angle of emergence

• A = Angle of the prism

• D = Angle of deviation

2. Variation of Angle of Deviation with Angle of Incidence

When the angle of incidence is gradually increased, the angle of deviation initially decreases. It reaches a minimum value and then starts increasing.

This variation can be represented by plotting a graph between the angle of incidence (i) along the X-axis and the angle of deviation (D) along the Y-axis. The resulting curve is approximately U-shaped.

The lowest point of the curve represents the angle of minimum deviation (Dₘ).

3. Condition for Minimum Deviation

When the prism is in the position of minimum deviation, the light ray passes symmetrically through the prism.

Under this condition:

• Angle of incidence = Angle of emergence (i = e)

• First angle of refraction = Second angle of refraction (r₁ = r₂)

• Each angle of refraction is equal to half the prism angle (r₁ = r₂ = A/2).

Therefore, the angle of minimum deviation is:

Dₘ = 2i − A

4. Formula for Refractive Index of the Prism

The refractive index (μ) of the prism material with respect to air can be calculated using the prism angle (A) and the angle of minimum deviation (Dₘ).

The formula is:

μ = sin[(A + Dₘ)/2] / sin(A/2)

where:

• μ = Refractive index of the prism material

• A = Angle of the prism

• Dₘ = Angle of minimum deviation

Thus, by determining the minimum deviation from the i–D graph and knowing the angle of the prism, the refractive index of the glass material can also be calculated.

Important: The minimum deviation occurs when the path of the light ray through the prism is symmetrical. This is the principle used in the present experiment.

 

Refraction through a prism- Angle of minimum deviation

Procedure

1. Fix a white sheet of paper on a drawing board using drawing pins or adhesive tape.

2. Place the glass prism on the sheet and trace its outline carefully. Mark the vertices of the prism as A, B and C.

3. Select one refracting face of the prism and draw a normal at a suitable point on that face.

4. Draw an incident ray making a suitable angle of incidence (i) with the normal. Place two optical pins vertically along this incident ray, keeping them sufficiently apart.

5. Replace the prism exactly along its traced outline. Looking through the other refracting face of the prism, place two more optical pins so that they appear in a straight line with the images of the first two pins. Avoid parallax while aligning the pins.

6. Remove the prism and the pins. Mark the positions of the pins and the points where the incident and emergent rays meet the prism surfaces.

7. Join the marked points to trace the incident ray, refracted ray inside the prism and emergent ray. Extend the incident ray forward to show the angle of deviation.

8. Measure the angle of incidence (i) and the angle of deviation (D) using a protractor. Record the readings in the observation table.

9. Repeat the experiment for different values of the angle of incidence, changing the direction of the incident ray each time. Record the corresponding angle of deviation for every observation.

10. Plot a graph by taking the angle of incidence (i) along the X-axis and the angle of deviation (D) along the Y-axis.

11. Draw a smooth curve through the plotted points. Identify the lowest point of the curve and determine the corresponding minimum angle of deviation (Dₘ).

12. Record the value of the minimum angle of deviation obtained from the graph.

13. If required, calculate the refractive index of the prism material using:

μ = sin[(A + Dₘ)/2] / sin(A/2)

Angle of Minimum Deviation- Observations

Angle of minimum deviation-Graph

The graph is plotted between the angle of incidence (i) along the X-axis and the angle of deviation (D) along the Y-axis. As the angle of incidence increases, the angle of deviation initially decreases, reaches a minimum value, and then increases.

The graph is therefore approximately U-shaped. The lowest point on the curve represents the angle of minimum deviation (Dₘ). At this point, the light ray passes symmetrically through the prism, so the angle of incidence is equal to the angle of emergence (i = e), and the two angles of refraction are equal (r₁ = r₂).

The minimum deviation is determined by drawing a horizontal line from the lowest point of the curve to the Y-axis and noting the corresponding value of the angle of deviation.

Conclusion: The lowest point of the i–D graph gives the angle of minimum deviation of the given prism.

Worked Calculation:

• Prism angle, A = 60°

• Minimum deviation, Dₘ = 37°

Refractive index:

Result:

The angle of minimum deviation of the given glass prism was determined by plotting a graph between the angle of incidence and the angle of deviation.

The minimum deviation obtained from the graph is ___37__°.

The refractive index of the prism material, calculated using the prism formula, is  1.498 (no unit).

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. When the angle of incidence (i) is equal to the angle of emergence (e), the light ray passes symmetrically through the prism. The angles of refraction inside the prism are also equal (r₁ = r₂ = A/2). Under this condition, the angle of deviation reaches its minimum value, called the angle of minimum deviation (Dm).

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Link:

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