PhysicsCBSE Class 12 · Practical, Section B, experiment 5

Angle of minimum deviation of a prism from the i-δ graph (Class 12 practical)

Updated 16 October 2026 · Fact-checked

Trace rays through a glass prism with pins for angles of incidence from 35° to 60°, and measure the angle of deviation δ for each. Plot δ against i: the δ at the lowest point of the curve is the angle of minimum deviation δm. At that point i = e and the ray inside runs parallel to the base.

Aim

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

Apparatus and material required

Drawing board
Triangular glass prism
White paper sheets and graph paper
Alpins
Drawing pins or adhesive tape
Protractor
Metre scale and a sharp pencil

Principle

A ray PQ falls on face AB of a prism at angle of incidence $i$ , refracts at angle $r_{1}$ , meets face AC at angle $r_{2}$ and emerges at angle $e$ . The angle of deviation $δ$ is the angle between the incident ray produced forward and the emergent ray produced backward. From the geometry,

$r_{1} + r_{2} = A$ and $δ = i + e - A$ .

As $i$ increases, $δ$ first decreases, reaches a least value $δ_{m}$ , then increases. At minimum deviation, the ray passes symmetrically: $i = e$ , $r_{1} = r_{2} = A /2$ , and the ray inside the prism is parallel to the base. Then

$n = \frac{sin ( \frac{A + δ _{m}}{2} )}{sin ( \frac{A}{2} )}$ .

Prism: angle of minimum deviation from the i-δ graph: formulas and key facts

Angles inside the prism: $r_{1} + r_{2} = A$
Angle of deviation: $δ = i + e - A$; Check each reading: i + e should equal A + δ.
At minimum deviation: $i = e, r_{1} = r_{2} = \frac{A}{2}, i = \frac{A + δ _{m}}{2}$
Refractive index (prism formula): $n = \frac{sin ( \frac{A + δ _{m}}{2} )}{sin ( \frac{A}{2} )}$
Key facts: i-δ graph: U-shaped curve, not a straight line
Take i above 35°
Take extra readings near the minimum
Minimum is flat, so draw the tangent parallel to the i-axis carefully
Image is brightest at minimum deviation
δm is larger for violet than for red light

Procedure

1Fix a white sheet on the drawing board. Draw a straight line XY across the middle, parallel to the length of the sheet.
2Mark points O₁, O₂, O₃ … on XY about 8 cm to 10 cm apart and draw a normal at each.
3Draw incident rays at O₁, O₂ … making angles of incidence of 35°, 40°, 45°, 50°, 55° and 60° with the normals, using a protractor. Write each angle on the sheet.
4Place the prism with face AB on XY and O₁ in the middle of AB. Draw its outline with a sharp pencil.
5Fix two pins P₁ and Q₁ vertically about 10 cm apart on the incident ray. Looking through the other face, fix pins R₁ and S₁ about 10 cm apart in line with the images of P₁ and Q₁.
6Remove the pins, circle the pin pricks and join R₁S₁ to get the emergent ray. Produce it backwards to meet the incident ray produced forward, and mark arrows on the rays.
7Measure the angle of deviation δ and the angle of the prism A with the protractor and write them on the diagram.
8Repeat for the other angles of incidence, using the same prism and the same angle A. Take two or three extra readings near the lowest δ.
9Plot δ (y-axis) against i (x-axis), draw a smooth curve, and read δm at its lowest point.

Observation table

Draw the table like this in your record. The numbers are sample readings to show how it is filled in; use your own.

Angle of incidence, emergence and deviation (A = 60°, least count of protractor 0.5°)
S. No.	i (°)	e (°)	δ (°)	Check: i + e (°)	Check: A + δ (°)
1	35	66.0	41.0	101.0	101.0
2	40	58.5	38.0	98.5	98.0
3	45	52.5	37.5	97.5	97.5
4	47	50.0	37.0	97.0	97.0
5	49	48.5	37.0	97.5	97.0
6	51	46.0	37.5	97.0	97.5
7	55	43.0	37.5	98.0	97.5
8	60	39.0	39.0	99.0	99.0

Sample readings for a glass prism of refractive index about 1.5, to show how the table is filled in; they are not real measurements. e and δ are measured separately, so i + e and A + δ differ by up to 0.5°, within the protractor's least count. Rows 4 to 6 are the extra readings near the minimum.

Calculation

Plot i on the x-axis and δ on the y-axis. Draw a smooth curve through the points, not straight segments between them.

1.Draw a tangent to the lowest part of the curve, parallel to the i-axis. It meets the δ-axis at 37.0°, so δm = 37.0°.
2.The lowest point is at i ≈ 48°; check: (A + δm)/2 = (60 + 37)/2 = 48.5°, and there e ≈ i, as expected.
3.Optional, refractive index: $n = \frac{sin 48.5°}{sin 30°} = \frac{0.7490}{0.5000} = 1.498 \approx 1.50$

Result

The angle of minimum deviation for the given prism is δm = ____° (sample: 37.0°). The i-δ graph shows that δ first decreases and then increases as i increases.

Precautions

Fix the alpins vertically, with their feet (or tips) in line.
Keep each pair of pins about 10 cm apart, so the rays are drawn accurately.
Use the same prism and the same refracting angle A for all readings.
Do not move the prism while fixing the pins for a reading.
Take angles of incidence above 35°, and extra readings near the minimum.
Draw a smooth free-hand curve, and the tangent at the minimum parallel to the i-axis.

Sources of error

Pins may not be exactly vertical, so the rays are drawn slightly wrong.
Errors in measuring the angles with the protractor.
The prism outline may shift if the prism moves while pins are fixed.
The minimum of the curve is flat, so δm is read with some uncertainty.

Viva questions with answers

Say your answer out loud first, then open the card. Examiners want one or two clear sentences, not a paragraph.

1.Define the angle of deviation.Show answer
The angle between the incident ray produced forward and the emergent ray produced backward.
2.What is the shape of the i-δ graph?Show answer
A U-shaped curve: δ first decreases as i increases, reaches a minimum δm, and then increases.
3.What happens at minimum deviation?Show answer
The ray passes symmetrically: the angle of incidence equals the angle of emergence, r₁ = r₂ = A/2, and the ray inside the prism is parallel to the base.
4.Write the relation between i, e, A and δ.Show answer
$δ = i + e - A$ , so i + e = A + δ.
5.Why are angles of incidence below about 35° avoided?Show answer
The ray may meet the second face at more than the critical angle and be totally internally reflected, so it does not emerge.
6.On what does the angle of minimum deviation depend?Show answer
On the angle of the prism, the refractive index of the material (and so the colour of light), and the medium around the prism.
7.Will δm be greater for red or for violet light?Show answer
For violet light, because glass has a larger refractive index for violet than for red.
8.How is refractive index found from δm?Show answer
$n = sin (\frac{A + δ _{m}}{2}) / sin (\frac{A}{2})$ .
9.If the prism is placed in water, what happens to δm?Show answer
It decreases, because the refractive index of glass relative to water is less than relative to air.
10.Why should the pins be about 10 cm apart?Show answer
The direction of a line through two points is found more accurately when the points are far apart.
11.Why do we take more readings near the minimum?Show answer
The curve is flat there, so closely spaced readings are needed to place the lowest point accurately.
12.What is the angle of the prism?Show answer
The angle between the two refracting faces of the prism, A.

Viva practice: these questions one at a time, with the answer hidden until you ask, and a tally of what to revise.

Common mistakes in the practical exam

The slips examiners see most often, and what to write instead.

Mistake: Joining the points with straight lines or drawing a sharp V.
The i-δ graph is a smooth curve with a flat bottom.
Do this: Draw one smooth free-hand curve through or close to all the points.
Mistake: Measuring δ between the emergent ray and the face of the prism.
Do this: Produce the incident ray forward and the emergent ray backward; δ is the angle between these two lines.
Mistake: Not checking i + e = A + δ.
Do this: Measure e too, and check each row; a large mismatch means a ray was drawn wrongly.
Mistake: Using a different face or vertex of the prism for some readings.
Do this: Mark the vertex A and always place the same face on XY.
Mistake: No arrowheads on the rays, or no angles written on the ray diagrams.
Do this: Mark arrows on the incident and emergent rays and write i, δ and A on each diagram.

Prism: angle of minimum deviation from the i-δ graph: frequently asked questions

Do I need to find the refractive index?

The CBSE aim asks only for the angle of minimum deviation. NCERT suggests finding n from δm as an additional exercise, and it is a common viva question.

Based on: CBSE Physics (042) curriculum 2026-27, Class XII practicals, Section B experiment 5; NCERT Laboratory Manual Physics Class XII, Experiment 13 (prism); NCERT Laboratory Manual Physics Class XII, Data section, Table DS 3 (refractive index)