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Glass Prism: Refraction, Angle of Minimum Deviation, Refractive Index, Dispersion of Light, and Complete CBSE Class 12 Guide

A comprehensive guide to the glass prism — refraction of light through a prism, derivation of prism formula, angle of minimum deviation, refractive index, i-d graph, dispersion of white light, spectrum, total internal reflection, and the CBSE Class 12 practical experiment.
21 July 2026 by
Glass Prism: Refraction, Angle of Minimum Deviation, Refractive Index, Dispersion of Light, and Complete CBSE Class 12 Guide
Krishan Kant
● CBSE Class 12 Physics — Ray Optics & Optical Instruments

Of all the optical instruments in a physics laboratory, the glass prism produces the most visually stunning demonstration in science: shine a narrow beam of white light into one face of a triangular glass prism, and out the other side emerges a beautiful rainbow — red, orange, yellow, green, blue, indigo, violet — fanned out in perfect sequence. This phenomenon, called the dispersion of white light, was first studied systematically by Sir Isaac Newton in 1666, when he used a prism to show that white light is not pure but is composed of all the colours of the visible spectrum.

The glass prism is far more than a colour-separator. It is a precision optical instrument used to measure the refractive index of glass, to study the refraction of light and Snell’s law, to understand the angle of minimum deviation, and to demonstrate total internal reflection. The prism experiment is a mandatory CBSE Class 12 Physics practical (Ray Optics, Chapter 9) in which students plot the i–d graph to determine the angle of minimum deviation and hence calculate the refractive index of the glass prism.

This guide covers the glass prism comprehensively: key terms, Snell’s law application at a prism surface, derivation of the prism formula, angle of minimum deviation, refractive index formula, the i–d graph, step-by-step experiment procedure, observation table, dispersion of light, total internal reflection, uses of prisms, and five CBSE exam-ready FAQs. All optical apparatus described is manufactured and supplied by AJKANT Overseas from Ambala, India.

Refractive Index of Glass Prism — Prism Formula
μ = sin[(A + Dᵖ) / 2] / sin(A / 2)
Valid at Minimum Deviation • A = Angle of Prism • Dᵖ = Angle of Minimum Deviation
μ
Refractive index of glass (dimensionless, typically 1.5–1.9)
A
Angle of the prism (apex angle, usually 60°)
Dᵖ
Angle of minimum deviation (from i–d graph)

1. What is a Glass Prism? Key Terms

A glass prism is a transparent optical element with flat, polished surfaces that refract (bend) light. The most common type used in school physics is the equilateral triangular prism — a prism whose cross-section is an equilateral triangle with all angles equal to 60°. When light travels from air into glass (denser medium), it bends towards the normal at the surface (refracts); when it exits glass into air, it bends away from the normal.

● Angle of the Prism (A)
The angle at the apex of the prism (the top vertex, between the two refracting surfaces). For an equilateral prism, A = 60°. Also called the apex angle or refracting angle.
● Angle of Incidence (i)
The angle between the incident ray and the normal at the first refracting surface of the prism. Measured from the normal drawn perpendicular to the surface at the point of incidence.
● Angle of Refraction (r)
The angle between the refracted ray (inside the prism) and the normal at the first surface (r₁), and the angle of the ray inside the prism at the second surface (r₂). At minimum deviation: r₁ = r₂ = A/2.
● Angle of Deviation (d or δ)
The angle between the original direction of the incident ray and the final direction of the emergent ray after passing through the prism. Depends on the angle of incidence i. The prism deviates the light towards its base.
● Angle of Minimum Deviation (Dᵖ or δᵖ)
The smallest value of the angle of deviation for a given prism and wavelength of light. Occurs when the refracted ray inside the prism is parallel to the base (i.e., r₁ = r₂ = A/2 and i₁ = i₂). Used to calculate the refractive index.
● Refractive Index (μ or n)
The ratio of the speed of light in vacuum to the speed of light in the glass medium: μ = c/v. Also equals the ratio sin(i)/sin(r) by Snell’s law. For common glass: μ ≈ 1.5. For flint glass: μ ≈ 1.7–1.9.
● Emergent Ray
The ray that exits the second refracting face of the prism. The emergent ray is on the same side as the base of the prism relative to the incident ray — the prism always deviates light towards its base.
● Critical Angle (C)
The angle of incidence (inside the glass, at the glass-air interface) above which total internal reflection occurs and no light escapes from the glass. For glass with μ = 1.5: sin C = 1/μ = 1/1.5, so C = 41.8°.

2. Refraction of Light Through a Prism — Snell’s Law

When a ray of light enters the first face of a prism, it is refracted (bent towards the normal) as it goes from air (less dense, μ = 1) into glass (denser, μ > 1). When it exits the second face, it is refracted again (bent away from the normal) as it goes from glass back into air. The net result is that the emergent ray is deviated from the original direction of the incident ray.

Snell’s Law at Each Refracting Surface
sin i / sin r = μ   ⇒   μ = sin i / sin r
At Surface 1: μ = sin i₁ / sin r₁ (air to glass, ray bends towards normal)
At Surface 2: μ = sin e / sin r₂ (glass to air, ray bends away from normal)
where i₁ = angle of incidence at surface 1, r₁ = angle of refraction at surface 1
e = angle of emergence, r₂ = angle of incidence at surface 2 (inside glass)

📈 Refraction Through a Prism — Ray Diagram

A (Apex, angle = 60 deg) / / / N1 / r1 \ r2 N2 | / --- \ | i1 / ray \ e | | ---/ inside \--- | Incident Emergent Ray Ray d = angle of deviation = (i1 - r1) + (e - r2) At minimum deviation: r1 = r2 = A/2, i1 = e Relation: r1 + r2 = A

Important geometric relations:

  • Inside the prism: r₁ + r₂ = A (sum of the two internal angles of refraction equals the apex angle)
  • Angle of deviation: d = (i₁ − r₁) + (e − r₂) = i₁ + e − A
  • Rearranging: i₁ + e = A + d

3. Prism Formula Derivation

At the condition of minimum deviation, the ray inside the prism travels parallel to the base of the prism. This means r₁ = r₂ = r (the angles of refraction at both surfaces are equal). Also, i₁ = e (angle of incidence equals angle of emergence).

Step-by-Step Derivation of Prism Formula
μ = sin[(A + Dᵖ)/2] / sin(A/2)
Step 1: At minimum deviation: i₁ = e = i (say) and r₁ = r₂ = r (say)
Step 2: From r₁ + r₂ = A:   r + r = A  ⇒  r = A/2
Step 3: From i₁ + e = A + Dᵖ:   i + i = A + Dᵖ  ⇒  i = (A + Dᵖ)/2
Step 4: Apply Snell’s law at surface 1: μ = sin i / sin r
Step 5: Substituting:  μ = sin[(A + Dᵖ)/2] / sin(A/2)

Worked Example: Equilateral prism (A = 60°), Dᵖ = 40°.
μ = sin[(60 + 40)/2] / sin(60/2) = sin 50° / sin 30° = 0.766 / 0.500 = 1.532

4. Angle of Minimum Deviation and Refractive Index

As the angle of incidence i increases from 0° to 90°, the angle of deviation d first decreases, reaches a minimum value Dᵖ (the angle of minimum deviation), and then increases again. This gives the characteristic U-shaped i–d curve.

Properties of the minimum deviation condition:

  • The refracted ray inside the prism is parallel to the base of the prism.
  • The angles of refraction at both surfaces are equal: r₁ = r₂ = A/2.
  • The angles of incidence and emergence are equal: i₁ = e = (A + Dᵖ)/2.
  • The prism and incident/emergent rays form an isosceles triangle.
  • The refractive index is given by the prism formula: μ = sin[(A + Dᵖ)/2] / sin(A/2).
Why is minimum deviation important? The prism formula μ = sin[(A+Dᵖ)/2] / sin(A/2) is valid only at the condition of minimum deviation. At other angles of incidence, the relationship between μ, i, and r is more complex. By finding Dᵖ experimentally (from the i–d graph), students can calculate the refractive index of any glass sample with high precision. This is why the prism experiment asks students to plot the i–d graph and locate the minimum point.

5. The i–d Graph (Angle of Incidence vs Angle of Deviation)

The i–d graph is plotted with the angle of incidence (i) on the x-axis and the angle of deviation (d) on the y-axis. The graph has a characteristic shape:

📊 Shape of the i–d Graph

d (Angle of Deviation) | | * * | * * | * * | * * | * * | * * | ** <--- Minimum point (D_m) | +----+----+----+----+----+----> i (Angle of Incidence) i_min i_max - The curve is U-shaped (parabolic) - The lowest point gives D_m (angle of minimum deviation) - Draw a smooth curve through all plotted points - Draw a horizontal tangent at the bottom of the curve - The value of d at the tangent point = D_m

To find Dᵖ from the graph: Draw the best smooth curve through all (i, d) points. Draw a horizontal tangent at the lowest point of the curve. The value of d at this tangent point is the angle of minimum deviation Dᵖ.

6. Experiment Procedure — Step-by-Step

Aim: To determine the angle of minimum deviation for a glass prism and calculate its refractive index.

  1. Measure the Angle of the Prism (A)
    Place the prism on a white sheet of paper. Draw the outline of the prism. Mark the two refracting faces (AB and AC) and the base (BC). Measure the angle A at the apex using a protractor. For a standard equilateral prism, A = 60°. Verify by measuring: if all three sides are equal, A = B = C = 60°.
  2. Set Up the Prism on the Drawing Board
    Fix a white sheet of paper on a drawing board. Place the prism on the paper with one refracting face (AB) facing the incident light source (a ray box or a narrow slit with a lamp). Draw the prism outline on the paper. Mark the position of the prism carefully — it must not shift during the experiment.
  3. Draw the Incident Ray at Angle i = 35° (First Reading)
    Draw a normal to face AB at the chosen point of incidence P. Draw the incident ray at angle i = 35° to this normal (using a protractor). Fix two pins P₁ and P₂ on the incident ray line. The pins must be at least 8 cm apart so the line is well-defined.
  4. Fix Pins on Emergent Side and Locate Emergent Ray
    Look through the second face (AC) of the prism for the images of pins P₁ and P₂. Fix two more pins P₃ and P₄ on the emergent side such that all four pins appear to be in a straight line (P₄, P₃ collinear with image of P₁, P₂). Remove the prism. Draw the emergent ray through P₃ and P₄. Extend incident and emergent rays to find their intersection — the angle between them is the angle of deviation d.
  5. Measure the Angle of Deviation d
    Using a protractor, measure the angle between the incident ray direction (extended) and the emergent ray direction. This is the angle of deviation d for this angle of incidence i = 35°. Record the values (i, d) in the observation table.
  6. Repeat for i = 40°, 45°, 50°, 55°, 60°, 65°
    Repeat steps 3–5 for at least 6 different angles of incidence (i = 35°, 40°, 45°, 50°, 55°, 60°, 65°). For each i, find the corresponding d and record in the observation table. Ensure the prism position does not shift between readings.
  7. Plot the i–d Graph and Find Dᵖ
    Plot all (i, d) points on graph paper. Draw a smooth freehand curve through the points. Draw a horizontal tangent at the lowest point of the curve. The d-value at the lowest point is the angle of minimum deviation Dᵖ. Read Dᵖ carefully from the graph.
  8. Calculate Refractive Index using Prism Formula
    Substitute A (measured in Step 1) and Dᵖ (from graph in Step 7) into the prism formula: μ = sin[(A + Dᵖ)/2] / sin(A/2). Calculate μ. Standard glass gives μ ≈ 1.5; denser glass gives higher values.

7. Observation Table

Angle of prism A = ______ °  |  Material of prism: Crown / Flint glass

S.No. Angle of Incidence
i (degrees)
Incident ray
direction (drawn)
Emergent ray
direction (drawn)
Angle of Deviation
d (degrees)
Remarks
135DoneDone____
240DoneDone____
345DoneDone____
450DoneDone____Near Dᵖ
555DoneDone____
660DoneDone____
765DoneDone____
Standard Result Format
Angle of minimum deviation Dᵖ = ______ ° (from i–d graph)
Refractive index μ = sin[(A + Dᵖ)/2] / sin(A/2) = sin[( ______ + ______)/2] / sin(______/2) = ______
Standard value of μ for crown glass = 1.52  |  Percentage error = |μᵇᵏᵉ − μᵃᴹᴿ| / μᵃᴹᴿ × 100%

8. Dispersion of White Light Through a Prism — Spectrum

When white light (which is a mixture of all visible wavelengths) passes through a glass prism, each colour (wavelength) is refracted by a different amount because the refractive index of glass depends on wavelength — this property is called dispersion. Violet light (shortest wavelength, ~380 nm) has the highest refractive index and is deviated most; red light (longest wavelength, ~750 nm) has the lowest refractive index and is deviated least.

● Violet ● Indigo ● Blue ● Green ● Yellow ● Orange ● Red

The splitting of white light into its component colours is called dispersion, and the band of colours produced is called the visible spectrum or rainbow spectrum (VIBGYOR: Violet, Indigo, Blue, Green, Yellow, Orange, Red).

Dispersive Power of Prism
ω = (μᵛ − μᵅ) / (μ − 1)
ω = dispersive power (dimensionless)  |  μᵛ = refractive index for violet light  |  μᵅ = refractive index for red light
μ = mean refractive index (usually for yellow light) = (μᵛ + μᵅ)/2
Higher dispersive power = greater separation between violet and red in the spectrum.
Flint glass has higher dispersive power than crown glass.
Newton’s prism experiment (1666): Newton showed that when a white-light spectrum is passed through a second, inverted prism, the colours recombine to form white light again. This proved that the prism does not “add” colours to the light — it only separates colours that were already present in white light. This experiment established that white light is a mixture of all colours of the spectrum.

9. Uses of Glass Prism

🌈
Spectrometer and Spectroscopy
Prisms are used in spectrometers to disperse light into its component wavelengths for spectral analysis. Each element emits a unique set of spectral lines (emission spectrum) that can be identified by their wavelengths, making prism spectrometers essential tools in chemistry, astronomy, and material science.
📷
Periscopes and Binoculars (Porro Prism)
Porro prisms use total internal reflection (TIR) to redirect light by 90° or 180° without any loss of intensity. Used in binoculars to fold the optical path and reinvert the image, and in submarine periscopes to see above water level. TIR gives 100% reflection, far better than any mirror.
🔭
Optical Fibre Communication
The principle of total internal reflection (TIR), which can be demonstrated with a prism, is the basis of optical fibre communication. Light signals are trapped inside the glass fibre by TIR and travel over thousands of kilometres without significant loss, carrying internet, telephone, and television signals.
🔯
Measuring Refractive Index
The glass prism experiment (finding Dᵖ and using the prism formula) is one of the most accurate methods to measure the refractive index of glass. This is used in optical engineering to characterise glass types, in gem testing to identify gemstones, and in quality control of optical components.
Beam Splitters and Polarisers
Special prisms (Nicol prism, Wollaston prism) split a beam of light into two polarised components. Used in polarimeters (to measure the rotation of polarised light by optically active substances such as sugar solutions), microscopes with polarised light, and mineralogy.
🎡
Decorative and Display Lighting
Crystal glass prisms and chandeliers use dispersion to create sparkling rainbow effects in interior lighting. Triangular prism pendants catch sunlight and project rainbow spectra on walls and ceilings, creating beautiful visual effects in homes and architectural spaces.

10. Frequently Asked Questions (FAQ)

Q1. What is the prism formula for refractive index?

The prism formula for refractive index is: μ = sin[(A + Dᵖ)/2] / sin(A/2), where μ is the refractive index of the glass, A is the angle of the prism (apex angle), and Dᵖ is the angle of minimum deviation. This formula is derived from Snell’s law applied at the condition of minimum deviation, where the refracted ray inside the prism is parallel to the base. At this condition, r₁ = r₂ = A/2 and i = e = (A+Dᵖ)/2. Applying Snell’s law: μ = sin i / sin r = sin[(A+Dᵖ)/2] / sin(A/2).

Q2. What is the angle of minimum deviation, and why is it important?

The angle of minimum deviation (Dᵖ) is the smallest value of the angle of deviation for a given prism and light wavelength. As the angle of incidence i is varied from small to large values, the angle of deviation d first decreases, reaches a minimum (Dᵖ), and then increases. The minimum occurs when the refracted ray inside the prism is parallel to the base (r₁ = r₂ = A/2, i = e). It is important because: (1) The prism formula μ = sin[(A+Dᵖ)/2]/sin(A/2) is valid only at this condition. (2) Dᵖ is found from the i–d graph by reading the d-value at the lowest point, making it an experimentally accessible quantity for calculating μ.

Q3. Why does a prism disperse white light into a spectrum?

A prism disperses white light into a spectrum because the refractive index of glass depends on the wavelength (colour) of light. Glass has a higher refractive index for shorter wavelengths (violet light, ~380 nm) and a lower refractive index for longer wavelengths (red light, ~750 nm). By Snell’s law (μ = sin i / sin r), a higher refractive index means a larger bending angle r is smaller), so violet light is bent more than red light when passing through the glass prism. This differential bending separates the colours into a rainbow spectrum: V-I-B-G-Y-O-R from most-bent to least-bent. This phenomenon is called dispersion, and it shows that white light is composed of all the colours of the spectrum.

Q4. What is the relation between the angle of prism and the angles of refraction inside it?

Inside a prism, the two angles of refraction (r₁ at the first surface and r₂ at the second surface) are related to the apex angle (A) of the prism by: r₁ + r₂ = A. This relationship comes from the geometry of the triangular prism: the refracted ray inside the prism makes angles r₁ and r₂ with the normals to the two surfaces, and the sum of these angles equals the apex angle of the prism. At minimum deviation (the special case used in the experiment): r₁ = r₂ = A/2, so the refracted ray inside is parallel to the base and the prism is in its most symmetric configuration.

Q5. What is total internal reflection, and how does a prism demonstrate it?

Total internal reflection (TIR) occurs when light travelling from a denser medium (glass) to a rarer medium (air) hits the interface at an angle greater than the critical angle (C), where sin C = 1/μ. At angles of incidence > C, no light escapes into air — all the light is reflected back inside the glass. A 45°-45°-90° right-angle prism demonstrates TIR: when a horizontal ray enters the vertical face and hits the hypotenuse at 45° (greater than the critical angle of ≈41.8° for glass), it reflects at 90°. Two such prisms are used in periscopes and binoculars to fold the light path. Porro prism systems in binoculars use TIR for 100% reflection efficiency (no energy loss, unlike a silvered mirror).

Source Optical Lab Equipment from Ambala

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