Lesson Note on Light Waves: Prism Refraction and Minimum Deviation for SSS 2

Class: Senior Secondary School 2 (SS2 / SSS 2)
Term: First Term
Week: 10
Age: 16 years
Duration: 45 minutes
Subject: Physics
Curriculum Theme: Waves (Optics)
Previous Lesson: Light Waves: Refraction, Snell’s Law and Total Internal Reflection.
Topic: LIGHT WAVES
Subject Matter: Refraction of light through triangular glass block (prism refraction), angle of minimum deviation (meaning and observation), totally reflecting prisms (uses)

Specific Objectives

By the end of the lesson, pupils should be able to:

Cognitive Domain:

• Define refraction of light through a triangular glass prism.
• Explain the concept of the angle of minimum deviation.
• State the formula relating refractive index, prism angle, and minimum deviation.
• List various uses of totally reflecting prisms.

Affective Domain:

• Appreciate the importance of accurate measurements in physics experiments.
• Demonstrate an interest in the practical applications of light.

Psychomotor Domain:

• Trace the path of light rays through a triangular glass block.
• Measure angles of incidence, refraction, and deviation in a prism experiment.
• Calculate the refractive index of a prism using the angle of minimum deviation formula.

Social Domain:

• Collaborate effectively in groups during practical activities.
• Communicate scientific observations and conclusions clearly.

Reference Materials

The following resources were used in planning this lesson:

• Senior Secondary Schools Education Curriculum
• State Unified Scheme of Work
• New School Physics by P.N. Okeke and M.W. Anyakoha

Instructional Materials

The teacher will teach this lesson with the aid of:

• Textbook
• Equipped laboratory (triangular glass prism, optical pins, drawing board, plain white paper, protractor, ruler, pencil)

Rationale for the Lesson

This lesson helps pupils understand how light behaves when it passes through different transparent materials like a prism. It enables them to grasp the principles behind phenomena like dispersion and total internal reflection, which are important for understanding various optical instruments and natural occurrences.

Prerequisite/Previous Knowledge

Pupils should have prior knowledge of the laws of refraction, critical angle, and total internal reflection.

Lesson Content/Board Summary

Refraction of Light through a Triangular Glass Block

Introduction to Prism Refraction

Refraction is the bending of light as it passes from one transparent medium to another of different optical density. A triangular glass prism causes light to bend twice, once upon entering and once upon exiting, resulting in a net deviation of the light ray.

The path of a light ray through a triangular glass prism involves:

• Incident Ray: The ray of light striking the first face of the prism.
• Refracted Ray: The ray of light inside the prism, bent towards the normal.
• Emergent Ray: The ray of light leaving the second face of the prism, bent away from the normal.
• Angle of Incidence (i₁): Angle between the incident ray and the normal at the first surface.
• Angle of Refraction (r₁): Angle between the refracted ray and the normal at the first surface.
• Angle of Refraction (r₂): Angle between the refracted ray and the normal at the second surface.
• Angle of Emergence (i₂ or e): Angle between the emergent ray and the normal at the second surface.
• Angle of Prism (A): The angle between the two refracting faces of the prism.
• Angle of Deviation (D): The angle between the incident ray and the emergent ray. It represents the total change in direction of the light.

The angle of deviation (D) is given by the formula: D = (i₁ + i₂) – A

Angle of Minimum Deviation (Dm)

The angle of minimum deviation (Dm) is the smallest angle through which a ray of light can be deviated by a prism. This occurs when the path of the light ray inside the prism is symmetrical, meaning the angle of incidence (i₁) is equal to the angle of emergence (i₂) and the two angles of refraction inside the prism (r₁ and r₂) are also equal.

At minimum deviation: i₁ = i₂ and r₁ = r₂

The refractive index (n) of the prism material can be calculated using the formula:

n = sin((A + Dm)/2) / sin(A/2)

Where:

• n = Refractive index of the prism material
• A = Angle of the prism
• Dm = Angle of minimum deviation

Worked Examples

Example 1: A glass prism has an angle of 60°. If the angle of minimum deviation through the prism is 38°, calculate the refractive index of the glass.

Solution:

Step 1: Identify the given values.

• Angle of prism (A) = 60°
• Angle of minimum deviation (Dm) = 38°

Step 2: Apply the formula for refractive index at minimum deviation.

n = sin((A + Dm)/2) / sin(A/2)

Step 3: Substitute the values into the formula.

n = sin((60° + 38°)/2) / sin(60°/2)

n = sin(98°/2) / sin(30°)

n = sin(49°) / sin(30°)

Step 4: Calculate the sine values and the refractive index.

n = 0.7547 / 0.5000

n ≈ 1.5094

Therefore, the refractive index of the glass is approximately 1.51.

Example 2: A prism has a refractive index of 1.5 and a refracting angle of 60°. Calculate the angle of minimum deviation.

Solution:

Step 1: Identify the given values.

• Refractive index (n) = 1.5
• Angle of prism (A) = 60°

Step 2: Apply the formula for refractive index at minimum deviation and rearrange to solve for Dm.

n = sin((A + Dm)/2) / sin(A/2)

1.5 = sin((60° + Dm)/2) / sin(60°/2)

1.5 = sin((60° + Dm)/2) / sin(30°)

Step 3: Isolate sin((60° + Dm)/2).

sin((60° + Dm)/2) = 1.5 × sin(30°)

sin((60° + Dm)/2) = 1.5 × 0.5

sin((60° + Dm)/2) = 0.75

Step 4: Find the angle whose sine is 0.75.

(60° + Dm)/2 = sin⁻¹(0.75)

(60° + Dm)/2 ≈ 48.59°

Step 5: Solve for Dm.

60° + Dm = 2 × 48.59°

60° + Dm = 97.18°

Dm = 97.18° – 60°

Dm = 37.18°

Therefore, the angle of minimum deviation is approximately 37.18°.

Totally Reflecting Prisms

Totally reflecting prisms are prisms that utilize the phenomenon of total internal reflection to change the direction of light rays without significant loss of intensity. They are typically made of glass and are designed so that light rays incident on one of their faces strike another face at an angle greater than the critical angle for the glass-air interface.

Most common totally reflecting prisms are isosceles right-angled prisms (angles 45°, 45°, 90°).

The following are uses of totally reflecting prisms:

• Periscopes: Used to see over or around obstacles by reflecting light through 90° or 180°.
• Binoculars: Used to magnify distant objects by folding the light path and inverting the image.
• Cameras: Used in some camera viewfinders to correct image orientation.
• Reflecting Telescopes: Used to direct light to the eyepiece.
• Optical Fibres: Though not prisms, they work on the principle of total internal reflection to transmit light over long distances.

Teaching Methods/Instructional Techniques

Discussion, Lecture, Demonstration, Question and Answer, Visual Aids

Instructional Procedures

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction
Teacher’s Activity: The teacher greets the pupils and reviews the previous lesson on the critical angle and total internal reflection. The teacher then introduces the new topic, “Refraction of Light through Triangular Glass Block,” by asking pupils what happens when light passes through a transparent block.
Pupils’ Activity: Pupils respond to the questions and recall prior knowledge. They listen attentively to the introduction of the new topic.
Learning Point: Pupils recall previous concepts and are prepared for the new lesson.

Step 2: Refraction through a Triangular Glass Prism

Time: 10 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher explains the path of light through a triangular glass prism, defining terms like incident ray, refracted ray, emergent ray, angle of incidence, angle of emergence, angle of deviation, and angle of the prism. The teacher draws a diagram on the board to illustrate these concepts.
Pupils’ Activity: Pupils observe the diagram, listen to the explanations, and ask questions for clarification. They copy the diagram and definitions into their notes.
Learning Point: Pupils understand the terms and ray path associated with light refraction through a prism.

Step 3: Practical Verification of Snell’s Law / Ray Tracing

Time: 10 minutes
Teaching Skill: Practical Guidance
Teacher’s Activity: The teacher guides pupils on how to set up an experiment to trace light rays through a triangular glass block using optical pins, drawing board, and plain paper. The teacher emphasizes the procedure for measuring angles of incidence, refraction, and deviation, and how this relates to Snell’s law.
Pupils’ Activity: Pupils, in groups, set up their apparatus and follow the teacher’s instructions to trace rays and measure angles, under supervision.
Learning Point: Pupils gain practical experience in observing and measuring refraction through a prism.

Step 4: Angle of Minimum Deviation

Time: 7 minutes
Teaching Skill: Explanation/Formula Derivation
Teacher’s Activity: The teacher explains the concept of the angle of minimum deviation (Dm) and the conditions under which it occurs (symmetrical path). The teacher presents the formula n = sin((A + Dm)/2) / sin(A/2) and explains each variable. The teacher solves Example 1 from the board summary.
Pupils’ Activity: Pupils listen to the explanation, copy the formula, and follow the steps of the solved example. They ask questions about the formula and its application.
Learning Point: Pupils understand the meaning of minimum deviation and its mathematical relationship to the refractive index.

Step 5: Totally Reflecting Prisms

Time: 5 minutes
Teaching Skill: Explanation/Discussion
Teacher’s Activity: The teacher discusses totally reflecting prisms, explaining that they use total internal reflection to redirect light. The teacher describes their common shapes (e.g., isosceles right-angled prisms) and lists their applications in various optical instruments like periscopes, binoculars, and cameras.
Pupils’ Activity: Pupils listen and note down the characteristics and uses of totally reflecting prisms.
Learning Point: Pupils learn about the practical applications of total internal reflection in prisms.

Step 6: Class Discussion/Problem Solving

Time: 3 minutes
Teaching Skill: Questioning/Application
Teacher’s Activity: The teacher leads a brief discussion on the differences between refraction through a prism and through a rectangular block. The teacher then guides pupils through solving Example 2 from the board summary, reinforcing the application of the minimum deviation formula.
Pupils’ Activity: Pupils participate in the discussion and actively engage in solving the problem, asking for help where needed.
Learning Point: Pupils deepen their understanding by applying concepts to solve problems.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

1. Define refraction of light through a triangular glass prism.
2. State two factors that affect the angle of deviation in a prism.
3. Explain what is meant by the angle of minimum deviation.
4. Calculate the refractive index of a glass prism with an angle of 60° if the angle of minimum deviation is 38°.
5. List three uses of totally reflecting prisms.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 2 minutes
Teaching Skill: Summarization
Teacher’s Activity: The teacher summarizes the key points of the lesson, reiterating the concepts of prism refraction, minimum deviation, and totally reflecting prisms. The teacher gives homework: research other optical instruments that use total internal reflection.
Pupils’ Activity: Pupils listen to the summary and note down the homework.
Learning Point: Pupils consolidate their understanding of the lesson and are given tasks for further learning.

Lesson Keywords

• Refraction – The bending of light as it passes from one medium to another.
• Prism – A transparent optical element with flat, polished surfaces that refract light.
• Angle of Deviation – The angle between the incident ray and the emergent ray after passing through a prism.
• Minimum Deviation – The smallest angle of deviation for a ray passing through a prism, occurring when the path inside the prism is symmetrical.
• Totally Reflecting Prism – A prism designed to cause total internal reflection, used to redirect light.
• Critical Angle – The angle of incidence beyond which total internal reflection occurs.

Differentiation

For pupils who grasp concepts quickly, the teacher can provide additional complex problems involving varying prism angles or different refractive indices. For pupils who need more support, the teacher can offer simplified diagrams, one-on-one guidance during practical sessions, or provide partially worked examples to complete.

Note for teachers using this lesson plan

Ensure that all practical materials are readily available and in good working condition before the lesson. Emphasize safety precautions during the experiment. Encourage pupils to draw neat and accurate diagrams. Pay close attention to pupils’ understanding of the minimum deviation condition as it is crucial for applying the formula correctly.