Questions: Geometric Optics and the Ray Approximation

Question 1

A physics student wants to predict where an image will form after light passes through a glass lens 5 cm in diameter. Which scenario would geometric optics FAIL to handle correctly?

• A. Tracing the image formed by the same lens
• B. Calculating the angle of refraction as light enters the glass
• C. Predicting the rainbow pattern when white light strikes a CD
• D. Finding the reflection angle of a laser beam off a flat mirror

Answer: (C)

A CD has microscopic grooves spaced on the order of visible light wavelengths (~500 nm). At that scale, diffraction dominates — the wave nature of light cannot be ignored — and geometric optics is silent about diffraction. Options A, B, and D all involve optical elements far larger than a wavelength, where the ray approximation is valid. The CD is the boundary case that exposes what geometric optics cannot do.

Question 2

The ray approximation underlying geometric optics is valid when which condition holds?

• A. The speed of light in the medium equals c
• B. The wavelength of light is much smaller than the optical elements it encounters
• C. The wavelength of light is much larger than the optical elements it encounters
• D. Light travels in a vacuum rather than through glass or water

Answer: (B)

The approximation treats light as rays rather than waves. This works only when the wave nature of light — wavelength-scale effects like diffraction — is negligible relative to the features of the optical system. Visible light has wavelengths of roughly 400–700 nm; a typical lens is centimeters across (tens of thousands of times larger), so the wave effects are imperceptible. When this scale separation collapses — such as at a tiny aperture or fine grating — diffraction dominates and rays are the wrong model.

Question 3

Geometric optics can explain the colored halos that sometimes appear around street lights on foggy nights.

• T. True
• F. False

Answer: False

Halos and coronas around lights in fog are caused by diffraction and interference of light interacting with water droplets near the wavelength of light — a wave-optics phenomenon. Geometric optics, which treats light as straight-line rays, cannot produce or predict these effects. This is exactly the kind of phenomenon the explainer cites as beyond geometric optics' reach.

Question 4

In geometric optics, a ray is always perpendicular to the wavefront it represents.

• T. True
• F. False

Answer: True

This is the defining geometric relationship: wavefronts are surfaces of constant phase, and rays point in the direction of energy propagation — which is always perpendicular (normal) to the wavefront. In a uniform medium, wavefronts are spheres (from a point source) or planes (from a distant source), and the rays fan outward radially or travel in parallel. Snell's law and the law of reflection describe how rays (and thus wavefronts) change direction at interfaces.

Question 5

Explain why geometric optics works well for designing a glass camera lens but fails to explain what a diffraction grating does to light.

Model answer: A camera lens is centimeters across — roughly 100,000 times larger than the wavelength of visible light — so wave effects (diffraction, interference) are negligible and rays model the light accurately. A diffraction grating has grooves spaced at the wavelength scale, where those wave effects dominate. Geometric optics assumes wavelength is negligible, so it cannot predict or describe diffraction — it would just model the grating as a flat surface and miss the phenomenon entirely.

The key is the ratio of feature size to wavelength. Geometric optics is valid when this ratio is very large; it breaks down when the ratio approaches 1. Understanding this boundary tells you exactly when to switch from ray tracing to wave optics — it is not a matter of preference but of which physics is actually happening at the scale of the device.