Ray Optics

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.

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

1. 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.

2. 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.

3. If $\lvert m\rvert > 1$, the image is:

   • A. smaller
   • B. the same size
   • C. magnified
   • D. always virtual

   Answer: C.

4. Short response: explain why sign convention must be stated before using the thin-lens equation.

Worked Example

An object is $0.40\ \text{m}$ from a convex lens with focal length $0.15\ \text{m}$. Find the image distance.

1. State the equation:

   $$\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$$

2. Substitute:

   $$\frac{1}{0.15} = \frac{1}{0.40} + \frac{1}{d_i}$$

3. 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.

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:

1. identify the model,
2. state the useful assumption,
3. identify a limitation,
4. judge whether the model is sufficient for the given purpose.