To Determine Angle of Minimum Deviation for a Given Prism

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

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.

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.

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,

Dm = angle of minimum deviation of a prism

A = angle of a prism

n = refractive index

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

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.

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°.

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.

Angle of Deviation in Prism Experiment Observations

The first six observations of the Experiment:

Angle of prism ‘A’ =.....

 Our observation Angle of the prism ∠A Angle of Deviation in Prism ∠Dm 1. 35° 2. 40° 3. 45° 4. 50° 5. 55° 6. 60°

Our calculations gave the following graph:

Question 1: What Precautions to be Taken While Performing the Angle of Minimum Deviation in the Prism Experiment?

Answer: 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:

1. The angle of incidence should always lie between 35° to 60°.

2. We should fix the pins vertically.

3. We should make sure that the distance between the two pins should not be less than 10 mm.

4. Arrowheads must be marked to represent the incident and emerging rays.

5. A similar angle of the prism should be used for all the observations.

6. Always use thin pinpricks.

7. Measurement of angles may get wrong, so be careful and accurate while performing the experiment.

Question 2: What is the Angle Between Two Surfaces of a Prism? What is the Angle of Refraction of a Prism?

Answer: 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.