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.
- 1. What is a Glass Prism? Key Terms
- 2. Refraction of Light Through a Prism — Snell’s Law
- 3. Prism Formula Derivation
- 4. Angle of Minimum Deviation and Refractive Index
- 5. i–d Graph (Angle of Incidence vs Angle of Deviation)
- 6. Experiment Procedure — Step-by-Step
- 7. Observation Table
- 8. Dispersion of White Light — Spectrum
- 9. Uses of Glass Prism
- 10. Frequently Asked Questions (FAQ)
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.
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.
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
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 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).
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
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.
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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°.
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Set Up the Prism on the Drawing BoardFix 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.
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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.
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Fix Pins on Emergent Side and Locate Emergent RayLook 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.
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Measure the Angle of Deviation dUsing 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.
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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.
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Plot the i–d Graph and Find DᵖPlot 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.
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Calculate Refractive Index using Prism FormulaSubstitute 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 |
|---|---|---|---|---|---|
| 1 | 35 | Done | Done | ____ | |
| 2 | 40 | Done | Done | ____ | |
| 3 | 45 | Done | Done | ____ | |
| 4 | 50 | Done | Done | ____ | Near Dᵖ |
| 5 | 55 | Done | Done | ____ | |
| 6 | 60 | Done | Done | ____ | |
| 7 | 65 | Done | Done | ____ |
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.
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).
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.
9. Uses of Glass Prism
Explore Related Optics Guides & Physics Lab Equipment
10. Frequently Asked Questions (FAQ)
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).
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.
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.
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.
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).
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