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

## Introduction

The Angle of the Deviation is the same angle, which is equal to the difference between the angle of incidence and the angle of refraction of a ray of light that is passing through the surface. This surface is between one medium and another of a different refractive index. In that case, a prism is considered as the minimum deviation position, in the time when the angle of incidence at the first surface, equals the angle of emergence, which is at the second surface.

## Aim

This experiment aims to determine a prism's the angle of minimum deviation by just plotting a graph between the two angles of incidence and deviation.

## Required material

There are a few required things, that are mandatory to experiment. They are, a drawing board, a white sheet of paper is mandatory, the whole process is dependent on a prism, so a prism (Gao *et al.* 2018). Some other instruments will be required for help, such as drawing pins, pencils, half-meter scale, office pins, protractor and lastly graph papers.

## Theory

The angle through which the emergent ray deviates from a direction of the incident ray, is referred to as the angle of deviation, d. On the other hand the angle of incidence is the angle that is between the impact direction and a solid surface(Gao *et al.* 2018).

When light travels from one medium to another medium and results in a deviation of the emergent ray from that of the incident ray, the refraction happens. The refractive index of the material that is used in the prism is-

$$\mathrm{n\:=\:\frac{[\frac{sin(A+Dm)}{2}]}{sin(\frac{A}{2})}}$$

In which $\mathrm{D_m}$ is referred to as the angle of minimum deviation and that A is denoted as the angle of prism.

**Figure 1: The angle of deviation**

## Process

At first a white sheet of paper needs to be fixed on the drawing board, and for that pins or tape can be used (stackexchange, 2022).

In the next step, in the middle of the paper, maintaining the proper length, one straight line, as XX’, has to be drawn. In order to measure the perfect distance 5cm, points need to be on the XX’ line in a manner Q1, Q2, and Q3 (Nwosu&Egesi, 2021).

In the next step, as per the diagram, normal such as $\mathrm{N_1Q_1\: N_2Q_2 \:N_3Q_3}$, need to draw on the points of $\mathrm{Q_1Q_2Q_3}$. Making angles respectively with the normals, straight lines have to draw.

Then, the corner of the prism has to be marked as A and for all observation, it should be considered as the edge of the prison (stackexchange, 2022).

For the next step, face the line AB on the top of XX’ and in the middle of the AB, Q1 should be the point. A boundary should be made of the prism. Maintaining the distance of 10mm for two or more office pins should be fixed vertically on the line of $\mathrm{R_1Q_1}$. Through the prism, face the AC and look for the image of points $\mathrm{P_1}$ and $\mathrm{P_2}$. Keeping only the eye open two images must be in a line. The other two office pins need to be fixed vertically just as shown in the diagram. Maintaining the distance of the pin as 10 cm is mandatory.

Then for Point $\mathrm{Q_2,\: Q_3}$ and many more priory mentioned processes needs to be repeated.

**Figure 2: Refraction through prism**

For measuring D in different cases, to get the emergent rays $\mathrm{S_1T_1}$, or more, a line needs to be drawn through $\mathrm{P_4}$ and $\mathrm{P_5}$ (Nwosu & Egesi, 2021). To meet produced incident ray, first produce the $\mathrm{T_1S_1,\: S_2T_2}$ and more. The angle needs to be measured which gives the angle of derivation and the value of the angle should be noted properly (learncbse, 2022). On the other hand, for measuring the A, The angle BAC that is in the boundary of the prism should be measured. The observation needs to be recorded.

## Observation from the experiment

A the angle of Prism is equal to,

Serial No. | The angle of incidence $\mathrm{\angle i}$ | Angle of deviation $\mathrm{\angle D}$ |
---|---|---|

1 | 35° | |

2 | 40° | |

3 | 45° | |

4 | 50° | |

5 | 55° | |

6 | 60° |

**Table 1: Observation table**

## The Final Calculation

**Figure 3: Graph between D and I**

Plot a graph between the angle of incidence and the angle of deviation, $\mathrm{\angle i}$ need to be taken along with the X-axis, in the same way, $\mathrm{\angle D}$needs to be taken along with the Y-axis (learncbse, 2022). The $\mathrm{D_m}$ can be found only from the graph that would be corresponding to the lowest point of the same.

The value of the $\mathrm{D_m}$ is-

Then the, $\mathrm{n\:=\:\frac{[\frac{sin(A+Dm)}{2}]}{sin(\frac{A}{2})}}$

## Final Result

The angle of the minimum deviation is -

Then the material of the prism’s Refractive index, that is n, will be

The graph indicated the increment the angle of incidence and then the decrement of the Angle of the deviation to attain the value of $\mathrm{D_m}$, and then lastly it increases as $\mathrm{\angle i}$ increased.

## Conclusion

The angle between 35 to 60, is the angle of incidence and needs to be maintained throughout the process. The pins must be placed vertically and the distance needs to be maintained as 10 mm. For the representation of the rays, the arrowhead must be marked. For all the observations, the angle of the prism should be the same. The pricks that are made by the pins can be thick enough and the angles can be measured wrongly.

## FAQ

**Q1. What is the angle of Deviation?**

Ans. The angle that is situated between the direction of the incident and the emergent ray, is referred to as the angle of Deviation.

**Q2. What is the angle of the Incident?**

Ans. The angle that is formed in between a ray on a surface and the impact direction, is called the Angle of the incident.

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