Ray Optics
Orientation
Lesson goal: use ray diagrams and thin-lens relationships to predict image location, size, orientation, and type.
The main discipline is to make the diagram and calculation agree. A ray diagram is evidence, not decoration.
Core Content
The ray model approximates light as travelling in straight-line paths through a uniform medium. Thin-lens and mirror equations are useful when the paraxial approximation is reasonable: rays stay close to the principal axis and angles are small.
Key equations:
$$\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$$
$$m = \frac{h_i}{h_o} = -\frac{d_i}{d_o}$$
| Evidence | Meaning |
|---|---|
| real image | rays physically converge and image can be projected on a screen |
| virtual image | rays appear to diverge from a point and cannot be projected |
| negative magnification | inverted image in the chosen convention |
| $\lvert m\rvert > 1$ | image is larger than object |
Concept Check
-
In a thin-lens ray diagram, a ray through the optical centre is usually drawn:
- A. as strongly curved
- B. approximately straight
- C. parallel then stopped
- D. backwards only
Answer: B.
-
A real image can be:
- A. projected onto a screen
- B. seen only by extending imaginary rays
- C. formed without any light rays
- D. created only by a plane mirror
Answer: A.
-
If $\lvert m\rvert > 1$, the image is:
- A. smaller
- B. the same size
- C. magnified
- D. always virtual
Answer: C.
-
Short response: explain why sign convention must be stated before using the thin-lens equation.
Applied Practice
Worked Example
An object is $0.40\ \text{m}$ from a convex lens with focal length $0.15\ \text{m}$. Find the image distance.
-
State the equation:
$$\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$$
-
Substitute:
$$\frac{1}{0.15} = \frac{1}{0.40} + \frac{1}{d_i}$$
-
Solve:
$$6.667 = 2.500 + \frac{1}{d_i}$$
$$d_i = 0.240\ \text{m}$$
Final answer: the image forms $0.240\ \text{m}$ on the opposite side of the lens. With this convention it is a real image.
Practice Problem
An object is $0.30\ \text{m}$ from a convex lens with focal length $0.10\ \text{m}$. Calculate image distance and magnification, then state whether your ray diagram should show a real or virtual image.
Deep Practice And Writing
Prompt: evaluate whether a thin-lens model is adequate for a classroom lens experiment. Your answer must mention the paraxial approximation and one source of image error.
Strong response pattern:
- identify the model,
- state the useful assumption,
- identify a limitation,
- judge whether the model is sufficient for the given purpose.
Tutor Context
Use this lesson context when the student asks about:
- ray diagrams,
- real and virtual images,
- thin-lens equation,
- magnification,
- sign conventions,
- model limitations.
Tutor should first check whether the student has a diagram that agrees with the calculation.
Useful tutor diagnostic:
Does your ray diagram show the rays physically meeting, or only appearing to meet when extended backward?
Maintenance Loop
Fast retrieval:
- A real image can be projected on a ______.
- $\lvert m\rvert > 1$ means the image is ______.
- The thin-lens equation should be used only after stating the ______.
Source Trace
This lesson is materialised from the existing textbook section, app lesson YAML, roadmap lesson, roadmap concept questions, and Module 3 notes. It is ready for conversion into a typed content manifest and panelled-course render block.