To Determine Angle of Minimum Deviation for a Given Prism

Dhristi JEE 2022-24

To Determine Minimum Deviation for Given Prism By Plotting Graph Between Angle of Incidence and Angle of Deviation

This article covers the procedure to determine the angle of minimum deviation for a prism. It contains the aim, Apparatus, theory, procedure, and observation, for determining the same.


To determine the minimum angle of deviation for a given prism, we need to plot a graph of the angle of incidence versus the angle of deviation. So, what does the angle of deviation mean?


Well! The angle of deviation of a prism is the angle that is obtained by finding the difference between the angle of incidence and the angle of refraction created by the light ray traveling from one medium to another that has a varying refractive index.


What is a Prism?

While looking at the sky, you might have wondered why there are rainbows during the rainy season? Did you ever see the work of a prism and wondered why it seems to create rainbows? Well, in this lesson you'll learn about prisms, how and why they work, and also the applications that you find in everyday phenomena.A prism is a thick transparent material just like glass or plastic, which has two flat surfaces that form an acute angle (less than 90°). 


White light contains seven colors of the rainbow. when it is passed through a prism, the colors of the rainbow emerge from the prism much like in the figure here. 


(Image will be Uploaded Soon)


We'll learn more about why a prism spreads white light out into the colors of the rainbow with an aim to determine angle of minimum deviation for a given prism.


Angle of Deviation in Prism

Theory of the angle of deviation in prism: A prism is a wedge-shaped object that is made from a refracting medium bounded by two plane faces inclined to each other at a certain angle. The two plane faces are the refracting faces and the angle between these faces is the angle of a prism (or the refracting angle).


To Determine the Angle of Minimum Deviation

To determine the angle of minimum deviation, let’s perform the angle of deviation of the prism experiment.


Aim of the Experiment:

To Determine the minimum angle of deviation of a prism.


Aim:

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


Apparatus:

Drawing board, meter scale, protractor, Pins(drawing and office), glass prism.


Materials or Apparatus Required:

  • A white sheet of paper

  • Drawing board

  • A prism

  • Drawing pins

  • A half-meter scale

  • Pencil

  • Office pins

  • Graph paper

  •  Protractor

  • Theory of the experiment:


The formula for the refractive index in the prism is given by:


\[n=\frac{sin(A+DM)/2}{sin(A/2)}\]


Here,


Here,


Dm = angle of minimum deviation of a prism

A = angle of a prismn = refractive index

Diagram for the refraction of the light-ray through the prism at various angles


(ImagewillbeUploadedSoon)


Steps to Perform the Angle of Deviation of Prism Experiment:

  1. Affix a white sheet of paper on the drawing board with the aid of drawing pins or tape.

  2. Now, draw a straight line XX’ lying parallel to the length of the paper approximately in the middle of the paper.

  3. Mark points Q1, Q2, Q3,… on the straight line XX’ at equal distances of around 5 cm.

  4. Draw normals, viz: N1Q1, N2Q2, N3Q3,… on points Q1, Q2, Q3,…  as shown in the above diagram.Draw straight lines R1Q1, R2Q2, R3Q3,… making angles of 40°, 45°, … 70°, respectively with the normals, after noting down the value of the angles on the paper. 

  5. Draw straight lines R1Q1, R2Q2, R3Q3,… making angles of 40°, 45°, … 70°, respectively with the normals, after noting down the value of the angles on the paper.

  6.  Mark one corner of the prism as A and consider it as the edge of the prism for all your observations.

  7. Put the prism with its refracting face AB in line XX’ and point Q1 in the middle of AB.

  8. Now, draw the boundary of the prism.

  9. Fix two or more office pins, viz: P1 and P2 vertically on the line R1Q1. The distance between the pins should be accurately 10 mm. Look at the images of points P1 and P2 via a face AC.

  10. Now, close your left eye and bring the opened right eye in line with the two images.

  11. Fix two office pins P3 and P4 vertically, and 15 cm apart such that the open right eye sees pins P4 and P3 and images of P2 and P1 in one straight line.

  12. Remove pins P3 and P4 and encircle their pricks (sharp points) on the paper.

  13. Now, repeat steps 7 to 12 with points Q2, Q3,… for i = 50°,…, 80°.


Theory:

The materials refractive in index of the given prism is denoted by 


n=\[\frac{sin(A+DM)/2}{sin(A/2)}\]


In which A is the angle of the prism and Dm is the angle of minimum deviation


(Image will be uploaded soon)


Procedure: - 

  • With the help of drawing tape, pins fix a white sheet of paper on the drawing board.

  • Draw a straight line XX' nearly in the middle of the paper parallel to the length of the paper.

  • On the straight line XX' mark points Q1, Q2, Q3, at suitable distances of 5cm.

  • On point Q1, Q2, Q3, draw normals and N1 1 and 2 Q2 and Q3 as represented in the diagram.

  • Draw straight lines are R1Q1, R2Q2,R3Q3.., construct angles of 35°,40°...60°   and with the normal strike the value of the angles on the paper .

  • On one corner of the prism,mark A, and take it as the edge of the prism for all the observations. 

  • Point Q1 in the middle of AB, and put the prism with its refracting face in line XX'.

  • The boundary of the prism should be marked.

  •  Put two or more office pins vertically on the line R1Q1 as P1 and P2. There should be a distance of 10 mm or more between the pins.

  • Through face AC observe the images of points P1 and P2.

  • Bring an open right eye in line with the two images by keeping your left eye close.

  •   Fix two office pins at 10 cm apart as P3 and P4 so that the open right eye sees images of P2 and P1 in one and P4 and P3  in one straight line .

  • On the paper encircle the pricks after removing the pins P3 and P4.

  • Repetition of Steps 7 to 13 with points Q2,Q3...for i=40°,....,60°.


To Measure Various Values of D, Follow these Four Steps:

  1. Draw straight lines via points P4 and P3 (pinpricks) to get emitting light rays, i.e., S1T1, S2T2, S3T3,……

  2. Produce T1S1, T2S2, T3S3, … in an inward direction in the boundary of the prism to meet produced incident rays, viz: R1Q1, R2Q2, R3Q3,… at points F1, F2, F3,…, respectively.

  3. Measure angles K1F1S1, K2F2S2, and K3F3S3,……... These give an angle of deviation; these are D1, D2, D3,…

  4. .Jot down values of these angles on the paper.


Now, to measure the angle of the prism, measure the angle BAC, and you get the value of A.Finally, record your observations.


 For Measuring D in Different Cases

  • Through pinpricks points P4 P3 draw a straight line to obtain emergent races S1T1,S2T2,S3T3…

  • To meet produced incident rays R1Q1,R2Q2,R3Q3…,at points F1,F2,F3,.... produce T1S1,T2S2,T3S3,... inward in the boundary of the prism.

  • By measuring the angles K1F1S1, K2F2S2, K3F3S3,... gives angle deviation D1,D2 D3….

  •  Write the values on the paper

For measuring a

  •  In the boundary of the prism measure angle BAC that gives angle A .

Record the Observations

Angle of Deviation in Prism Experiment Observations

The first six observations of the Experiment:Angle of prism ‘A’ =.....


Our observation

Angle of the prism angle A

Angle of deviation in prism angle Dm

1.

35°


2.

40°


3.

45°


4.

50°


5.

55°


6.

60°



Our calculations gave the following graph:


(Image will be Uploaded Soon)


Observation: 

  1. Type of prism = equilateral glass prism.

  2. The angle of prism = 60'    

  3. Table for variation of the angle of deviation with the angle of incidence


S.No.

Angle of incidence

Angle of deviation

1.

35'


2.

40'


3.

45'


4.

50'


5.

55'


FAQs on To Determine Angle of Minimum Deviation for a Given Prism

1.What is a prism shape?

A prism shape is a 3D shape that contains a constant cross section.  Both the ends are connected by rectangular sides and have the same 2D shape .The two ends are the same shape and size, meaning if you were to cut the shape in half, both pieces would look the same. A 2D shape with flat edges is a prism and some of the examples are rectangular prism, square prism, octagon prism and triangular prism.

2.What is prism and antiprism?

A regular prism consists of two regular N-sided polygons joined together by N squares. A regular antiprism consists of two regular N-sided polygons joined together by 2N equilateral triangles. The Square Prism and the Triangular Antiprism are the Cube and the Octahedron, respectively. The remaining regular prisms and antiprisms are closely related to Archimedean solids in the sense that they are convex polyhedra whose faces are regular polygons of two or more types that meet in the same pattern around each vertex.

3.Is a pyramid a prism?

A pyramid is a three-dimensional  structure Which has triangular  sites  joined at a vertex known as Apex and has one base  and its polygon in shape .  On the other hand, a 3D structure having two bases and rectangular sides is  known as a prism.Prism and Pyramid both are three-dimensional polyhedron shaped structures and the major difference lies in their base.

4.What are the different types of prisms?

A prism has polished surfaces that help in the refraction of light placed on one side of the prism and can be seen from the other side. Also, the cross-section in a prism is the same on all its sides. The shape of its base determines the type of prism. Few examples are hexagonal prisms, triangular prisms, pentagonal prisms and so on. In geometry and Optics prism is of utmost importance. It plays a vital role in the studies related to the splitting of the light, reflection and refraction.

5.What Precautions to be Taken While Performing the Angle of Minimum Deviation in the Prism Experiment?

A subject like Physics demands great practice on the theoretical parts and applying the knowledge practically requires the following precautions to be taken care of:The angle of incidence should always lie between 35° to 60°.We should fix the pins vertically. We should make sure that the distance between the two pins should not be less than 10 mm.Arrowheads must be marked to represent the incident and emerging rays.A similar angle of the prism should be used for all the observations.Always use thin pinpricks.Measurement of angles may get wrong, so be careful and accurate while performing the experiment.

6.What is the Angle Between Two Surfaces of a Prism? What is the Angle of Refraction of a Prism?

We know that the angle between two surfaces of a prism is known as refracting angle or the angle of prism. However, in a prism, a ray of light goes through two refractions and the result is deviation. The Ray of light passing through the prism is parallel to the base of the prism. The angle of refraction inside the transparent material of the prism is equal to half of the angle of the prism. A prism bears a very small refracting ∠A. A ray is an incident on the face of the prism in such a way that the angle of incidence ‘i’ is very small.

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