Class 10th Science Chapter 10 – The Human Eye and the Colourful World | Refraction of Light Through a Prism

The Human Eye and the Colourful World

Refraction of Light Through a Prism

प्रिज्म से प्रकाश का अपवर्तन

Class 10 Science | CBSE + Foundation + Competitive

🔺 Refraction of Light Through a Prism

1. Introduction | परिचय

Refraction is the change in direction of propagation of light when it passes obliquely from one transparent medium to another because its speed changes.

प्रकाश का अपवर्तन वह घटना है जिसमें प्रकाश एक पारदर्शी माध्यम से दूसरे पारदर्शी माध्यम में तिरछे प्रवेश करता है तो उसकी चाल में परिवर्तन के कारण उसकी दिशा बदल जाती है।

A prism is a transparent refracting medium bounded by two plane surfaces inclined to each other.

प्रिज्म एक पारदर्शी अपवर्तक माध्यम है जिसकी दो समतल अपवर्तक सतहें एक-दूसरे से कोण पर झुकी होती हैं।

2. What is a Prism? | प्रिज्म क्या है?

A triangular glass prism is commonly used to study refraction and dispersion of light.

A prism has two plane refracting surfaces inclined to each other. The angle between these two refracting surfaces is called the angle of prism (A).

3. Important Terms Related to Prism

Term	Meaning
Refracting surfaces	The two plane surfaces through which light enters and emerges.
Angle of prism (A)	Angle between the two refracting surfaces.
Base of prism	The side opposite the refracting angle.
Angle of incidence (i)	Angle between incident ray and normal at first surface.
Angle of refraction (r₁)	Angle between refracted ray and normal at first surface.
Angle of emergence (e)	Angle between emergent ray and normal at second surface.
Angle of deviation (δ)	Angle between the direction of the incident ray produced forward and the emergent ray.

4. Refraction Through a Prism | प्रिज्म में अपवर्तन

When a ray of light enters a glass prism from air, it passes from a rarer medium to a denser medium and bends towards the normal.

When the ray leaves the prism and enters air, it passes from a denser medium to a rarer medium and bends away from the normal.

Thus, the light ray undergoes refraction at both surfaces of the prism.

5. Deviation of Light by a Prism | प्रिज्म द्वारा प्रकाश का विचलन

A prism changes the direction of a light ray because the ray is refracted at two inclined surfaces.

The emergent ray is deviated from its original direction. This angular change is called the angle of deviation (δ).

For a conventional prism, the emergent ray is deviated generally towards the base of the prism.

δ = i + e − A

Where:
δ = angle of deviation
i = angle of incidence
e = angle of emergence
A = angle of prism

6. Relation Between Prism Angles

A = r₁ + r₂

Here:
A = angle of prism
r₁ = angle of refraction at first surface
r₂ = angle of refraction at second surface

7. Minimum Deviation | न्यूनतम विचलन

As the angle of incidence is gradually changed, the angle of deviation first decreases, reaches a minimum value and then increases.

The smallest value of the angle of deviation is called the angle of minimum deviation (δₘ).

At minimum deviation:

i = e

r₁ = r₂ = A/2

δₘ = 2i − A

Important CBSE Point: At minimum deviation, the path of the ray through the prism is symmetrical with respect to the prism.

8. Refractive Index of Prism Material

For a prism placed in air, the refractive index of the prism material can be related to the angle of prism and minimum deviation by:

μ = sin[(A + δₘ)/2] ÷ sin(A/2)

This formula is especially useful for numerical problems involving a prism, its angle and minimum deviation.

9. Numerical Example 1

Question: A prism has angle A = 60° and the angle of minimum deviation is 40°. Find the angle of incidence at minimum deviation.

At minimum deviation:
δₘ = 2i − A

40° = 2i − 60°
2i = 100°
i = 50°

10. Numerical Example 2

Question: For a prism, i = 50°, e = 45° and A = 60°. Find the angle of deviation.

Using:
δ = i + e − A

δ = 50° + 45° − 60°
δ = 35°

11. Numerical Example 3

Question: A prism has A = 60° and δₘ = 30°. Find the refractive index of the prism material.

μ = sin[(A + δₘ)/2] ÷ sin(A/2)

μ = sin[(60° + 30°)/2] ÷ sin30°
μ = sin45° ÷ sin30°
μ = 0.707 ÷ 0.5
μ ≈ 1.414

12. Prism and Dispersion | प्रिज्म एवं वर्ण-विक्षेपण

A prism can also separate white light into its constituent colours. This phenomenon is called dispersion of light.

Dispersion occurs because the refractive index of a transparent material generally depends on the wavelength of light.

Thus different colours are deviated by different amounts when white light passes through a prism.

13. Why Does a Prism Deviate Different Colours Differently?

The refractive index of the prism material is wavelength-dependent.

Shorter wavelengths generally experience a larger refractive index in ordinary transparent glass than longer wavelengths.

Therefore violet light is deviated more than red light in ordinary glass.

Colour	Approximate Wavelength Trend	Deviation in Ordinary Glass
Red	Longest among visible colours	Least
Orange	Shorter than red	More than red
Yellow	Intermediate	Intermediate
Green	Intermediate	Intermediate
Blue	Shorter	More
Indigo	Shorter	More
Violet	Shortest among visible colours	Maximum

14. Refraction vs Dispersion

Refraction	Dispersion
Bending/change in direction of light when it enters another medium.	Separation of white light into its constituent colours.
Caused by change in speed and direction.	Occurs because refractive index depends on wavelength.
Can occur with monochromatic light.	Requires polychromatic/white light for colour separation.
Example: Light bending in glass.	Example: VIBGYOR formation by prism.

15. Important Formulae

A = r₁ + r₂

δ = i + e − A

At minimum deviation: i = e

r₁ = r₂ = A/2

δₘ = 2i − A

μ = sin[(A + δₘ)/2] ÷ sin(A/2)

16. 30 MCQs | बहुविकल्पीय प्रश्न

Q1. A prism is primarily used to study:

(A) Refraction and dispersion of light

(B) Sound production

(C) Electric current only

(D) Magnetism only

Answer: A

Q2. The angle between the two refracting surfaces of a prism is called:

(A) Angle of deviation

(B) Angle of prism

(C) Angle of emergence

(D) Critical angle

Answer: B

Q3. When light travels from air into glass, it generally bends:

(A) Away from normal

(B) Along the surface

(C) Towards normal

(D) It does not bend

Answer: C

Q4. When light emerges from glass into air, it generally bends:

(A) Towards normal

(B) Along normal

(C) It stops

(D) Away from normal

Answer: D

Q5. The angle between the original direction of incident light and emergent ray is called:

(A) Angle of deviation

(B) Angle of prism

(C) Angle of refraction

(D) Angle of incidence

Answer: A

Q6. The relation for angle of prism is:

(A) A = i + e

(B) A = r₁ + r₂

(C) A = δ + i

(D) A = e − i

Answer: B

Q7. The formula for angle of deviation is:

(A) δ = A + i + e

(B) δ = A − i − e

(C) δ = i + e − A

(D) δ = i − e + A

Answer: C

Q8. At minimum deviation:

(A) i > e

(B) i < e

(C) r₁ > r₂

(D) i = e

Answer: D

Q9. At minimum deviation, the path of light through a prism is:

(A) Symmetrical

(B) Completely random

(C) Parallel to base only

(D) Perpendicular to the base

Answer: A

Q10. At minimum deviation, r₁ and r₂ are:

(A) Unequal

(B) Equal

(C) Zero always

(D) Greater than A

Answer: B

Q11. Dispersion of white light occurs because:

(A) All colours have exactly the same refractive index

(B) Light stops inside the prism

(C) Refractive index depends on wavelength

(D) Glass produces light

Answer: C

Q12. Which colour is deviated most by an ordinary glass prism?

(A) Red

(B) Yellow

(C) Green

(D) Violet

Answer: D

Q13. Which colour is deviated least by an ordinary glass prism?

(A) Red

(B) Violet

(C) Blue

(D) Indigo

Answer: A

Q14. The sequence of colours obtained from white light is commonly remembered as:

(A) GIBVYOR

(B) VIBGYOR

(C) ROYVIBG

(D) YORVIBG

Answer: B

Q15. The base of a triangular prism is opposite the:

(A) Incident ray

(B) Emergent ray

(C) Refracting angle

(D) Normal

Answer: C

Q16. The refractive index of a material is related to:

(A) Only mass

(B) Only density in every situation

(C) Sound frequency

(D) Speed of light in the material

Answer: D

Q17. If A = 60° and δₘ = 40°, then i at minimum deviation is:

(A) 50°

(B) 40°

(C) 30°

(D) 20°

Answer: A

Q18. If i = 50°, e = 45° and A = 60°, δ is:

(A) 25°

(B) 35°

(C) 45°

(D) 55°

Answer: B

Q19. At minimum deviation, if A = 60°, r₁ equals:

(A) 60°

(B) 45°

(C) 30°

(D) 15°

Answer: C

Q20. The emergent ray from a prism is generally deviated towards:

(A) Apex only

(B) Incident surface

(C) Normal only

(D) Base

Answer: D

Q21. A prism has two:

(A) Inclined refracting surfaces

(B) Parallel refracting surfaces

(C) Curved surfaces only

(D) Metallic surfaces

Answer: A

Q22. Refraction is caused mainly by change in:

(A) Mass of light

(B) Speed of light

(C) Charge of light

(D) Temperature of the observer

Answer: B

Q23. Dispersion separates white light into:

(A) Sound waves

(B) Heat rays

(C) Constituent colours

(D) Electrons

Answer: C

Q24. Which colour generally has the longest wavelength in visible light?

(A) Violet

(B) Blue

(C) Green

(D) Red

Answer: D

Q25. Which colour generally has the shortest wavelength in visible light?

(A) Violet

(B) Red

(C) Yellow

(D) Orange

Answer: A

Q26. The formula μ = sin[(A + δₘ)/2] / sin(A/2) is used for:

(A) Lens power

(B) Refractive index of prism material

(C) Mirror magnification

(D) Electric resistance

Answer: B

Q27. If A = 60° and δₘ = 30°, the refractive index is approximately:

(A) 1.0

(B) 1.2

(C) 1.414

(D) 2.5

Answer: C

Q28. Which statement is correct?

(A) Refraction occurs only in prisms

(B) Dispersion is reflection

(C) All colours are deviated equally by glass

(D) Different wavelengths can have different refractive indices

Answer: D

Q29. At minimum deviation, the incident and emergent angles are:

(A) Equal

(B) Always zero

(C) Always 90°

(D) Unequal

Answer: A

Q30. The main reason for different colours emerging at different angles is:

(A) Different masses of photons

(B) Wavelength-dependent refractive index

(C) Different temperatures of colours

(D) Different brightness

Answer: B

17. 30 Subjective Questions with Answers

2 Marks Q1. What is a prism?

A prism is a transparent refracting medium bounded by two plane refracting surfaces inclined to each other.

2 Marks Q2. Define angle of prism.

The angle between the two refracting surfaces of a prism is called the angle of prism (A).

2 Marks Q3. What is angle of deviation?

The angle between the original direction of the incident ray and the emergent ray is called the angle of deviation.

2 Marks Q4. What happens when light enters a glass prism from air?

It passes from a rarer to a denser medium and generally bends towards the normal.

2 Marks Q5. What is minimum deviation?

The smallest value of the angle of deviation obtained when the angle of incidence is varied is called the angle of minimum deviation.

3 Marks Q6. Explain refraction through a prism.

Light is refracted at both surfaces of the prism. It bends towards the normal on entering glass and away from the normal while emerging into air. The emergent ray is deviated from its original direction.

3 Marks Q7. Write the relation between A, r₁ and r₂.

The relation is:

A = r₁ + r₂

where A is the prism angle and r₁, r₂ are the two angles of refraction inside the prism.

3 Marks Q8. Write the formula for angle of deviation.

δ = i + e − A

3 Marks Q9. What happens at minimum deviation?

At minimum deviation, i = e and r₁ = r₂ = A/2. The path of the ray through the prism is symmetrical.

3 Marks Q10. Why does a prism deviate light?

The two refracting surfaces of a prism are inclined to each other. Therefore, light is refracted at both surfaces and its direction changes.

4 Marks Q11. Explain dispersion of white light through a prism.

White light contains different wavelengths. The refractive index of glass depends on wavelength, so different colours travel through the prism with different speeds and are deviated by different amounts. The colours spread out to form a spectrum.

4 Marks Q12. Why is violet deviated more than red in an ordinary glass prism?

Violet has a shorter wavelength than red. In ordinary glass, shorter wavelengths generally have a higher refractive index. Hence violet is refracted and deviated more than red.

4 Marks Q13. What is the significance of minimum deviation?

Minimum deviation represents the smallest angular deviation produced by the prism. At this condition the ray path is symmetrical and i = e. It is also used to determine the refractive index of the prism material.

4 Marks Q14. Differentiate between refraction and dispersion.

Refraction is the change in direction of light when it passes between media. Dispersion is the separation of polychromatic light into different colours because the refractive index varies with wavelength.

4 Marks Q15. Define angle of incidence, angle of emergence and angle of deviation.

Angle of incidence is the angle between incident ray and normal at the first surface. Angle of emergence is the angle between emergent ray and normal at the second surface. Angle of deviation is the angular change between the original direction and emergent direction.

5 Marks Q16. Derive the expression δ = i + e − A.

At the first surface, deviation is i − r₁. At the second surface, deviation is e − r₂. Therefore total deviation:

δ = (i − r₁) + (e − r₂)
δ = i + e − (r₁ + r₂)

Since A = r₁ + r₂:
δ = i + e − A

5 Marks Q17. Explain minimum deviation through a prism.

When the angle of incidence is varied, the angle of deviation decreases to a minimum value and then increases. At minimum deviation, the path through the prism becomes symmetrical. Therefore i = e and r₁ = r₂ = A/2.

5 Marks Q18. Explain why white light splits into colours in a prism.

White light contains many wavelengths. The refractive index of prism material is different for different wavelengths. Therefore each colour travels at a different speed inside the prism and is deviated by a different amount. This produces a spectrum of colours.

5 Marks Q19. Explain the important terms associated with a prism.

Important terms include angle of prism, refracting surfaces, base, angle of incidence, angles of refraction, angle of emergence and angle of deviation. The angle of prism is between the two refracting surfaces.

5 Marks Q20. Calculate δ if i = 55°, e = 45° and A = 60°.

δ = i + e − A

δ = 55° + 45° − 60°
δ = 40°

6 Marks Q21. Derive the refractive index formula for a prism at minimum deviation.

At minimum deviation:
i = e
r₁ = r₂ = A/2

Also:
δₘ = 2i − A
Therefore:
i = (A + δₘ)/2

Using Snell's law for air to prism:
μ = sin i / sin r

Substituting:
μ = sin[(A + δₘ)/2] ÷ sin(A/2)

6 Marks Q22. Explain refraction through a prism with a labelled ray diagram.

A ray entering from air into glass bends towards the normal. It then travels inside the prism and meets the second surface. On emerging into air it bends away from the normal. Due to the inclined surfaces, the emergent ray is deviated towards the base. The relevant angles are i, r₁, r₂, e, A and δ.

6 Marks Q23. Explain dispersion and write the order of colours.

Dispersion is the splitting of white light into constituent colours when it passes through a prism. The commonly observed order is:

Violet → Indigo → Blue → Green → Yellow → Orange → Red

Violet deviates most and red deviates least in ordinary glass.

6 Marks Q24. Explain minimum deviation and its conditions.

Minimum deviation is the minimum angular deviation produced by a prism. At this condition the path of light through the prism is symmetrical. Hence i = e and r₁ = r₂ = A/2.

6 Marks Q25. Explain the difference between a prism and a glass slab.

A glass slab has parallel refracting surfaces, whereas a prism has inclined refracting surfaces. A slab generally produces a lateral displacement and the emergent ray is parallel to the incident ray. A prism changes the direction of the emergent ray and produces angular deviation. A prism can also produce dispersion of white light.

6 Marks Q26. A prism has A = 60° and δₘ = 40°. Find i and r at minimum deviation.

At minimum deviation:
δₘ = 2i − A
40° = 2i − 60°
2i = 100°
i = 50°

Since r = A/2:
r = 60°/2
r = 30°

6 Marks Q27. Explain why the refractive index depends on wavelength.

The interaction of electromagnetic radiation with matter depends on frequency or wavelength. In ordinary transparent materials, the refractive index varies with wavelength, so different colours of visible light travel at different speeds in the material and undergo different refractions.

6 Marks Q28. Explain the complete path of a ray through a triangular prism.

The ray first strikes the first refracting surface and bends towards the normal while entering glass. It then travels through the prism and strikes the second refracting surface. While leaving glass and entering air, it bends away from the normal. Because the surfaces are inclined, the emergent ray is deviated from the original direction.

6 Marks Q29. Explain the relation among A, δ, i, e, r₁ and r₂.

The important relations are:

A = r₁ + r₂
and
δ = i + e − A

At minimum deviation:
i = e
r₁ = r₂ = A/2

6 Marks Q30. Explain the practical importance of studying prism refraction.

Prism refraction helps us understand bending and deviation of light. It is important for studying dispersion, spectroscopy, optical instruments and the wavelength dependence of refractive index. Prism-based systems are also used in several optical applications.

18. Assertion–Reason Questions

Q1. Assertion: A prism deviates a ray of light from its original direction.
Reason: The two refracting surfaces of a prism are inclined to each other.

Answer: Both Assertion and Reason are true, and the Reason correctly explains the Assertion.

Q2. Assertion: At minimum deviation, the angle of incidence equals the angle of emergence.
Reason: The path of light through the prism is symmetrical at minimum deviation.

Answer: Both statements are true, and the Reason correctly explains the Assertion.

Q3. Assertion: Violet light is deviated more than red light by ordinary glass.
Reason: The refractive index of ordinary glass is generally higher for shorter wavelengths.

Answer: Both statements are true, and the Reason correctly explains the Assertion.

Q4. Assertion: A glass slab and a prism always produce the same angular deviation.
Reason: The refracting surfaces of a glass slab are parallel.

Answer: Assertion is false, Reason is true.

Q5. Assertion: Dispersion is caused by wavelength-dependent refractive index.
Reason: Different wavelengths can undergo different amounts of refraction in the same material.

Answer: Both statements are true, and the Reason correctly explains the Assertion.

19. HOTS Questions | उच्च स्तरीय चिंतन

HOTS 1. Why does a prism produce angular deviation while a parallel-sided glass slab generally does not produce the same net angular deviation?

A prism has inclined refracting surfaces, so the second refraction does not cancel the first direction change completely. In a parallel-sided slab, the two surfaces are parallel and the emergent ray becomes parallel to the incident ray.

HOTS 2. At minimum deviation, why is the path of light symmetrical?

The minimum-deviation condition occurs when the incidence and emergence angles become equal. Consequently the two internal refraction angles are also equal, making the path symmetrical with respect to the prism.

HOTS 3. If a prism is illuminated with monochromatic red light instead of white light, will a spectrum be produced?

No. Monochromatic red light has essentially one wavelength, so it does not split into a visible spectrum of different colours. It will mainly undergo refraction and deviation.

HOTS 4. Why can a prism separate colours whereas a plane mirror cannot?

A prism refracts light and its refractive index depends on wavelength, so different colours are deviated differently. A plane mirror mainly reflects light without producing wavelength-dependent angular separation like a prism.

HOTS 5. If the angle of incidence is continuously increased from a low value, what happens to the deviation near minimum deviation?

The deviation initially decreases as the angle of incidence is increased, reaches a minimum value, and then increases again.

20. Diagram Labelling Practice

Label: Incident Ray, Refracted Ray, Emergent Ray, Normal, A, i, r₁, r₂, e and δ.

21. CBSE Golden Points ⭐

• Prism is a transparent refracting medium with inclined plane surfaces.
• The angle between the refracting surfaces is called angle of prism A.
• Light bends towards the normal when entering glass from air.
• Light bends away from the normal when emerging from glass into air.
• Light is refracted twice in a prism.
• A prism produces angular deviation.
• A = r₁ + r₂
• δ = i + e − A
• At minimum deviation, i = e.
• At minimum deviation, r₁ = r₂ = A/2.
• At minimum deviation, the ray path is symmetrical.
• Dispersion occurs because refractive index depends on wavelength.
• Violet is deviated most and red least in ordinary glass.
• VIBGYOR represents the visible spectrum order from shorter to longer wavelength.
• Red has the longest wavelength among the standard visible-colour sequence.
• Violet has the shortest wavelength among the standard visible-colour sequence.
• A prism and glass slab are different because their refracting surfaces have different geometry.
• A glass slab generally gives a laterally displaced emergent ray parallel to the incident ray.
• A prism generally gives angular deviation.

22. Memory Tricks | याद रखने की ट्रिक्स

🔺 PRISM

P = Prism → Two Inclined Surfaces

Inclined surfaces → Deviation

📐 ANGLE RELATION

A = r₁ + r₂

A याद रखें → अंदर के दोनों refraction angles का योग।

↪️ DEVIATION

δ = i + e − A

Incident + Emergent − Prism Angle

🎯 MINIMUM DEVIATION

Minimum → Symmetry

i = e
r₁ = r₂

🌈 DISPERSION

VIBGYOR

Violet → Maximum deviation
Red → Minimum deviation

📏 WAVELENGTH

Red → Long wavelength

Violet → Short wavelength

23. One-Minute Revision | एक मिनट में पूरा Topic

• 🔺 Prism → Transparent refracting medium with inclined surfaces.
• 📐 A = Angle of Prism
• ↘️ Air → Glass → Towards Normal
• ↗️ Glass → Air → Away from Normal
• 🔄 Prism → Refraction at Two Surfaces
• ↪️ δ = i + e − A
• 📌 A = r₁ + r₂
• 🎯 Minimum Deviation → i = e
• 🎯 Minimum Deviation → r₁ = r₂ = A/2
• 🌈 Dispersion → White Light → VIBGYOR
• 🟣 Violet → Maximum Deviation
• 🔴 Red → Minimum Deviation
• 🌈 Dispersion → Refractive Index depends on Wavelength
• 📚 Prism → Deviation + Dispersion

24. Final Summary | अंतिम सारांश

A prism is a transparent refracting medium with two inclined plane surfaces. When light enters a prism, it is refracted at the first surface and again at the second surface.

The total angular change in the direction of light is called the angle of deviation.

The important relations are:

A = r₁ + r₂
δ = i + e − A

At minimum deviation, the path of light is symmetrical and:

i = e
r₁ = r₂ = A/2

A prism can also disperse white light into its constituent colours because the refractive index of the material depends on wavelength. In ordinary glass, violet is deviated more than red.

Therefore, the study of prism refraction is important for understanding refraction, deviation, minimum deviation, refractive index and dispersion of light.

The Human Eye and the Colourful World
Refraction of Light Through a Prism
प्रिज्म से प्रकाश का अपवर्तन

Class 10 Science | CBSE + Foundation + Competitive