Questions: Dispersion and Wavelength-Dependent Refraction

Question 1

White light enters a glass prism. Which color is deflected the most upon exiting, and why?

• A. Red, because it has the longest wavelength and interacts most strongly with glass
• B. Green, because it is in the middle of the visible spectrum
• C. Violet, because it has the highest refractive index in the glass
• D. All colors deflect equally — the prism only sorts them spatially after exit

Answer: (C)

In normal dispersion, shorter wavelengths (higher frequency) drive electron oscillations closer to resonance, producing stronger interactions and a higher refractive index. Violet light has the highest n and therefore bends the most according to Snell's law. Red light has the lowest n and bends the least. Option D is incorrect — the angular separation occurs at each glass-air interface, not after exit.

Question 2

A glass lens produces 'chromatic aberration' — different colors focus at slightly different distances. What property of glass directly causes this?

• A. Glass absorbs shorter wavelengths more strongly than longer ones
• B. The refractive index of glass varies with wavelength, so each color refracts by a different amount
• C. The speed of light in vacuum is different for different colors
• D. Glass surfaces reflect longer wavelengths more than shorter ones

Answer: (B)

Chromatic aberration is a direct consequence of dispersion: because n varies with wavelength, different colors are refracted by different amounts at each lens surface and come to focus at different points. This is the same physics as a prism separating colors. Option C is wrong — all light travels at the same speed c in vacuum; the difference arises inside the glass. Option A (differential absorption) affects intensity, not focus.

Question 3

In normal dispersion, red light travels more slowly through glass than violet light does.

• T. True
• F. False

Answer: False

In normal dispersion, violet (shorter wavelength) has a higher refractive index than red. Since v = c/n, a higher n means a lower speed. Therefore violet light travels more slowly through glass than red light — the opposite of what the statement claims. This is counterintuitive because we often think of 'energetic' blue/violet light as 'faster,' but inside a dispersive medium, it is actually slower.

Question 4

Dispersion occurs because different wavelengths of light interact differently with the electrons in a material, resulting in wavelength-dependent propagation speeds.

• T. True
• F. False

Answer: True

This is the physical mechanism of dispersion. Light drives oscillations of the bound electrons in the material; higher-frequency (shorter-wavelength) light drives oscillations closer to the electrons' natural resonance frequency, producing stronger coupling and more slowing. This wavelength-dependent interaction is captured by the wavelength-dependent refractive index n(λ), which is the macroscopic signature of microscopic electron-photon coupling.

Question 5

In a rainbow, why does red appear on the outer arc and violet on the inner arc, given that violet has a higher refractive index in water than red does?

Model answer: Each water droplet refracts and internally reflects sunlight, dispersing it by color. Violet light, having a higher n, bends more sharply at the entry and exit surfaces, causing it to exit at a smaller angle from the incoming sunlight direction (~40°). Red light bends less and exits at a larger angle (~42°). When you look at the sky, droplets at ~42° from the antisolar point return red light to your eye; droplets at ~40° return violet. Because larger angles correspond to higher positions in the arc, red is on the outside (top) and violet on the inside.

The key is relating refractive index to exit angle via Snell's law and the geometry of the spherical droplet. Higher n → more bending at each surface → steeper internal path → different exit angle. The correspondence between exit angle and position in the visible arc (larger angle = higher in sky for primary rainbow) places red at the outside. This is not obvious — it requires tracing rays through the droplet geometry — but it follows directly from n_violet > n_red.