Lesson Note on Light Waves: Dispersion, Lenses and Lens Formula for SSS 2

Class: Senior Secondary School 2 (SS2 / SSS2)
Term: First Term
Week: 11
Age: 16 years
Duration: 45 minutes
Subject: Physics
Curriculum Theme: Light and Waves
Previous Lesson: Light Waves: Prism Refraction and Minimum Deviation.
Topic: LIGHT WAVES
Subject Matter: Dispersion of white light (splitting into spectrum), refraction of light through converging and diverging lenses (bending and focusing), images formed by lenses (ray diagrams and characteristics), lens formula (verification using illuminated object)

Specific Objectives

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

Cognitive Domain:

• Describe the dispersion of white light and identify the colours of the spectrum.
• Explain the difference between converging and diverging lenses.
• State the lens formula and explain the meaning of each variable.

Affective Domain:

• Appreciate the natural phenomenon of light dispersion.
• Show interest in practical activities involving lenses and light.

Psychomotor Domain:

• Set up an apparatus to demonstrate the dispersion of white light.
• Draw simple ray diagrams to show image formation by converging and diverging lenses.
• Outline the procedure for verifying the lens formula experimentally.

Social Domain:

• Work collaboratively during practical demonstrations and discussions.

Reference Materials

The following resources were used in planning this lesson:

• Senior Secondary Schools Education Curriculum
• State Unified Scheme of Work
• New School Physics for Senior Secondary Schools

Instructional Materials

The teacher will teach this lesson with the aid of:

• A triangular glass prism
• A white light source (e.g., torchlight or sunlight)
• Converging (convex) and diverging (concave) lenses
• Optical bench
• An illuminated object (e.g., a cross-wire gauze with a lamp)
• A screen
• A meter rule
• Textbook
• Equipped laboratory

Rationale for the Lesson

This lesson helps pupils understand how white light splits into colours and how lenses are used to form images. This knowledge is important for understanding optical instruments like cameras, microscopes, and even the human eye, and for appreciating natural phenomena like rainbows.

Prerequisite/Previous Knowledge

Pupils have a basic understanding of light, its propagation, reflection, and refraction through plane surfaces.

Lesson Content/Board Summary

LIGHT WAVES

Dispersion of White Light

Dispersion is the phenomenon where white light splits into its constituent colours when it passes through a transparent medium like a glass prism. This happens because different colours of light travel at slightly different speeds in the medium, causing them to refract at different angles.

The band of colours produced is called a spectrum. The colours of the visible spectrum are:

• Red
• Orange
• Yellow
• Green
• Blue
• Indigo
• Violet (ROYGBIV)

Refraction of Light through Converging and Diverging Lenses

A lens is a transparent optical device that focuses or disperses light rays by means of refraction.

• Converging Lens (Convex Lens): This lens is thicker in the middle and thinner at the edges. It converges parallel rays of light to a single point called the principal focus (F).
• Diverging Lens (Concave Lens): This lens is thinner in the middle and thicker at the edges. It diverges parallel rays of light, making them appear to come from a single point (virtual principal focus) on the same side as the object.

Images Formed by Lenses

Images formed by lenses can be located and characterized using ray diagrams. Key rays used are:

• A ray parallel to the principal axis passes through the principal focus after refraction (for converging lens) or appears to diverge from the principal focus (for diverging lens).
• A ray passing through the optical centre goes undeviated.
• A ray passing through the principal focus becomes parallel to the principal axis after refraction (for converging lens) or appears to be directed towards the principal focus (for diverging lens).

Image characteristics include:

• Real or Virtual
• Inverted or Erect
• Magnified, Diminished, or Same Size

Lens Formula and Magnification

The lens formula relates the object distance (u), image distance (v), and focal length (f) of a lens:

1/f = 1/u + 1/v

Where:

• f = focal length of the lens (positive for converging lens, negative for diverging lens).
• u = object distance (always positive).
• v = image distance (positive for real images, negative for virtual images).

Sign Conventions:

• Distances measured in the direction of light are positive.
• Distances measured against the direction of light are negative.
• Focal length of a converging lens is positive, diverging lens is negative.
• Real images have positive image distances, virtual images have negative image distances.

Magnification (M): The ratio of the image height (h’) to the object height (h), or the ratio of image distance (v) to object distance (u).

M = h’/h = v/u

Verification of Lens Formula (Practical Procedure)

The lens formula can be verified experimentally using an optical bench, an illuminated object, a converging lens, and a screen.

1. Place the illuminated object at one end of the optical bench.
2. Place the converging lens at a known position.
3. Adjust the screen until a sharp, clear image of the object is formed.
4. Measure the object distance (u), image distance (v), and record them.
5. Repeat the experiment for several different object distances.
6. Calculate the focal length (f) for each set of (u, v) values using the lens formula (1/f = 1/u + 1/v).
7. Find the average focal length. This average focal length should be approximately constant, verifying the formula.

Worked Examples

Example 1: An object is placed 30 cm in front of a converging lens of focal length 20 cm. Calculate the position and nature of the image.

Step 1: Identify given values and formula.
Given: u = +30 cm (object distance is always positive)
f = +20 cm (converging lens, so focal length is positive)
Formula: 1/f = 1/u + 1/v

Step 2: Substitute values into the formula to find v.
1/20 = 1/30 + 1/v
1/v = 1/20 – 1/30
1/v = (3 – 2) / 60
1/v = 1/60
v = +60 cm

Step 3: State the nature of the image.
Since v is positive, the image is real. The image is formed 60 cm from the lens on the opposite side of the object. For a real image formed by a converging lens, it is typically inverted. Magnification M = v/u = 60/30 = 2. So, the image is real, inverted, and magnified.

Example 2: An object 5 cm tall is placed 15 cm in front of a diverging lens of focal length 10 cm. Determine the position, nature, and height of the image.

Step 1: Identify given values and formula.
Given: u = +15 cm
f = -10 cm (diverging lens, so focal length is negative)
h = 5 cm (object height)
Formula: 1/f = 1/u + 1/v

Step 2: Substitute values into the formula to find v.
1/(-10) = 1/15 + 1/v
-1/10 = 1/15 + 1/v
1/v = -1/10 – 1/15
1/v = (-3 – 2) / 30
1/v = -5/30
1/v = -1/6
v = -6 cm

Step 3: State the nature and calculate the height of the image.
Since v is negative, the image is virtual. It is formed 6 cm from the lens on the same side as the object. For a diverging lens, the image is always virtual, erect, and diminished.

Magnification M = v/u = -(-6)/15 = 6/15 = 0.4
Image height h’ = M * h = 0.4 * 5 cm = 2 cm

Thus, the image is virtual, erect, diminished, and 2 cm tall.

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 asks questions about their previous knowledge of light, such as “What is light?” and “How does light travel?”. The teacher then introduces the topic of Light Waves, focusing on dispersion and lenses, and states the learning objectives.
Pupils’ Activity: Pupils respond to the questions and listen attentively to the introduction of the topic and objectives.
Learning Point: Pupils recall prior knowledge of light and are prepared for the new topic.

Step 2: Dispersion of White Light

Time: 8 minutes
Teaching Skill: Demonstration/Explanation
Teacher’s Activity: The teacher demonstrates the dispersion of white light using a triangular glass prism and a white light source. The teacher points out the spectrum formed and explains why dispersion occurs.
Pupils’ Activity: Pupils observe the demonstration carefully and identify the colours of the spectrum (ROYGBIV). They ask questions for clarification.
Learning Point: Pupils understand the phenomenon of dispersion and the formation of a spectrum.

Step 3: Converging and Diverging Lenses

Time: 8 minutes
Teaching Skill: Explanation/Identification
Teacher’s Activity: The teacher explains the characteristics of converging (convex) and diverging (concave) lenses, showing physical examples of each. The teacher describes how each type of lens affects parallel rays of light.
Pupils’ Activity: Pupils examine the lenses, identify their types, and understand their basic functions in converging or diverging light.
Learning Point: Pupils can differentiate between converging and diverging lenses based on their shape and effect on light.

Step 4: Image Formation by Lenses

Time: 8 minutes
Teaching Skill: Explanation/Illustration
Teacher’s Activity: The teacher explains the rules for drawing ray diagrams for both converging and diverging lenses. The teacher illustrates how to draw ray diagrams to locate and characterize images formed by lenses on the board.
Pupils’ Activity: Pupils observe the illustrations and practice drawing simple ray diagrams in their notebooks, identifying the characteristics of the images formed.
Learning Point: Pupils learn how to use ray diagrams to determine the position and nature of images formed by lenses.

Step 5: Lens Formula

Time: 6 minutes
Teaching Skill: Lecture/Problem Solving
Teacher’s Activity: The teacher introduces the lens formula (1/f = 1/u + 1/v), explaining each variable and the sign conventions. The teacher works through the first example on the board, applying the formula and explaining the steps.
Pupils’ Activity: Pupils copy the formula and sign conventions into their notes and follow the steps of the worked example.
Learning Point: Pupils understand the lens formula and its application in calculating image positions.

Step 6: Verification of Lens Formula (Practical Guidance)

Time: 5 minutes
Teaching Skill: Guidance/Discussion
Teacher’s Activity: The teacher outlines the experimental procedure for verifying the lens formula using an optical bench, illuminated object, lens, and screen. The teacher discusses the necessary measurements and calculations.
Pupils’ Activity: Pupils listen and ask questions about the experimental setup and procedure, preparing for a potential practical session.
Learning Point: Pupils understand the practical steps involved in verifying the lens formula.

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 dispersion of white light.
2. List the colours of the spectrum in their correct order.
3. Distinguish between a converging lens and a diverging lens.
4. An object is placed 40 cm from a converging lens with a focal length of 15 cm. Calculate the image distance and state the nature of the image.

Pupils’ Activity: Pupils answer orally and in writing.
Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 1 minute
Teaching Skill: Summarization
Teacher’s Activity: The teacher summarizes the key points of the lesson, reiterating the importance of dispersion and lenses in daily life. The teacher assigns homework, which includes drawing ray diagrams for different object positions for both types of lenses.
Pupils’ Activity: Pupils listen to the summary and copy down the homework.
Learning Point: Pupils consolidate their learning and are given tasks to reinforce understanding.

Lesson Keywords

• Dispersion – The splitting of white light into its constituent colours.
• Spectrum – The band of colours produced when white light is dispersed.
• Converging lens – A lens that converges parallel rays of light to a single point.
• Diverging lens – A lens that diverges parallel rays of light.
• Focal length – The distance between the optical centre of a lens and its principal focus.
• Lens formula – The relationship between object distance, image distance, and focal length (1/f = 1/u + 1/v).

Differentiation

For pupils who are struggling, the teacher will provide simplified ray diagram templates and guide them through step-by-step calculations for the lens formula. Advanced pupils will be challenged to explore magnification calculations and investigate real-world applications of different lens types, such as in telescopes or microscopes.

Note for teachers using this lesson plan

Ensure that the laboratory equipment is functional and readily available for demonstrations. Emphasize the sign conventions carefully when teaching the lens formula, as this is a common area of confusion for pupils. Encourage pupils to draw neat and accurate ray diagrams, as they are fundamental to understanding image formation.