Questions: Refractive Index: Definition and Wavelength Dependence

Question 1

A glass prism is illuminated with white light. Which color is refracted (bent) the most as it enters the glass?

• A. Red, because it has the longest wavelength and the most energy to push through the material
• B. Violet, because it has the shortest wavelength and therefore the highest refractive index in glass
• C. Green, because it is in the middle of the visible spectrum where glass absorbs least
• D. All colors are refracted equally because the prism is made of uniform glass throughout

Answer: (B)

The Cauchy equation n(λ) ≈ A + B/λ² shows that shorter wavelengths produce higher refractive indices. Violet light (λ ≈ 400 nm) has a higher n in glass than red light (λ ≈ 700 nm), so by Snell's law (n₁ sin θ₁ = n₂ sin θ₂) violet bends more sharply at the interface. Option A is the common misconception — wavelength and energy don't directly control bending; the refractive index does. Option D is wrong because n varies with wavelength even in homogeneous glass, which is the entire point of dispersion.

Question 2

A camera produces colored fringes around bright edges in its images. An optical engineer wants to eliminate this chromatic aberration. Which approach addresses the root cause?

• A. Using a lens made from a single glass type with the highest possible refractive index
• B. Adding an anti-reflective coating to all lens surfaces
• C. Using a doublet: combining two glass types with different dispersion curves so their wavelength-dependent bending partially cancels
• D. Reducing the lens aperture to block wavelengths at the spectrum edges

Answer: (C)

Chromatic aberration exists because n varies with wavelength — different colors focus at slightly different distances. The fix must address this wavelength dependence directly. A doublet uses crown glass (lower dispersion) and flint glass (higher dispersion) whose dispersion curves run in opposite directions for the same wavelengths, so their combined effect is nearly the same bending for all visible wavelengths. Option A makes aberration worse (higher n doesn't help if dispersion remains). Options B and D address reflections and intensity, not wavelength-dependent focusing.

Question 3

In most transparent optical materials, red light travels faster through the material than violet light.

• T. True
• F. False

Answer: True

Speed in a medium is v = c/n. Red light has a longer wavelength, so the Cauchy equation gives it a lower refractive index than violet light. Lower n means higher speed (v = c/n), so red light travels faster through glass or water than violet light. This is directly related to why violet bends more: higher n means slower speed at the interface, which corresponds to more bending via Snell's law.

Question 4

The refractive index of a material is a single fixed constant that characterizes the material's optical properties, independent of the color of light used.

• T. True
• F. False

Answer: False

This is the central misconception this topic corrects. The refractive index depends on wavelength — this wavelength dependence is called dispersion. The Cauchy equation n(λ) ≈ A + B/λ² shows n changes with λ. Glass has n ≈ 1.512 for red light and n ≈ 1.532 for violet light — a ~1% difference that is small but physically significant, producing the rainbow pattern from a prism and chromatic aberration in lenses. Textbooks sometimes give a single n value for a material only as an approximation for a specific wavelength (usually the sodium D line at 589 nm).

Question 5

Explain why a glass prism separates white light into its component colors, using the definition of refractive index and its relationship to wavelength.

Model answer: White light is a mixture of all visible wavelengths. The refractive index n of glass is higher for shorter wavelengths (violet, ~400 nm) than for longer wavelengths (red, ~700 nm) — captured by n(λ) ≈ A + B/λ². Since Snell's law n₁ sin θ₁ = n₂ sin θ₂ determines bending angle, and n differs for each wavelength, each color bends by a different amount when entering the prism. Violet bends most, red bends least, and the intermediate wavelengths spread between them. This wavelength-dependent refraction physically separates the originally overlapping colors into a spatial spectrum.