Dispersion & Refractive Index vs Wavelength Quiz

Concept: dispersion as n(λ). When refractive index depends on wavelength, different colours travel at different speeds. That makes their refraction angles differ, producing colour separation.

Concept: normal dispersion. For typical glass in the visible range, n is slightly larger for shorter wavelengths (blue/violet) than for longer wavelengths (red). A larger n means slower speed and generally more bending.

Concept: speed–index relation v = c/n. A larger refractive index means a smaller speed in the medium. Since n_blue is larger, blue travels slower than red in that material.

Concept: higher refractive index → more refraction toward the normal. At the boundary, the colour with the larger n experiences stronger bending. Since n_blue > n_red, blue bends more.

Concept: definition of refractive index. Refractive index is defined by n = c/v. Rearranging gives v = c/n, linking speed reduction to refractive index.

Concept: v = c/n. Using c ≈ 3.0×10^8 m/s, v = 3.0×10^8 / 1.50 = 2.0×10^8 m/s. This shows how refractive index reduces light speed in materials.

Concept: v = fλ with frequency fixed. Each colour keeps its frequency when entering a medium, but the speed depends on wavelength through n(λ). Because λ = v/f, different speeds for different colours imply different wavelengths in the medium.

Concept: frequency continuity at an interface. The oscillation rate is set by the source and must match across the boundary. The medium changes speed and wavelength, not the frequency.

Concept: λ = v/f. If v decreases while f stays the same, λ must decrease. That’s why light’s wavelength is shorter inside higher-index materials.

Concept: normal dispersion trend. In typical glass, shorter wavelengths have slightly higher refractive index than longer wavelengths. Therefore, as wavelength increases, n decreases slightly.

Concept: two-step dependence (refraction + dispersion). Snell’s law shows refraction depends on refractive index. Since refractive index depends on wavelength, different colours refract at different angles, producing separation.

Concept: higher n → stronger bending. A higher refractive index means the wave slows more in the medium. That increased slowing corresponds to greater refraction toward the normal.

Concept: chromatic aberration from dispersion. Because n differs by colour, the lens bends blue and red by different amounts. That changes focal length slightly for each colour, creating different focus positions.

Concept: wavelength-dependent focal length. Dispersion makes refractive index vary with wavelength, changing the lens’s bending power for each colour. This leads to coloured fringes or blur when colours do not focus together.

Concept: chromatic aberration correction. Achromatic designs combine materials so their dispersions partially cancel, improving colour focus alignment. Stopping down reduces the contribution of outer rays and can make colour fringing less noticeable.

Concept: deviation order in normal dispersion. Red light typically refracts less than violet in glass, so it deviates least. Violet deviates most, so the spread usually runs from red (least) to violet (most).

Concept: spectroscopy and characteristic wavelengths. Elements emit or absorb light at specific wavelengths, producing distinct lines. Dispersion separates these wavelengths so the lines can be observed and matched to particular elements.

Concept: spectral separation. The purpose of a spectroscope is to spread light out by wavelength. A prism does this via dispersion, while a grating does it via interference, but both create a spectrum.

Concept: strength of dispersion depends on dn/dλ. If n varies a lot across the visible range, different colours experience larger differences in bending. That produces a wider spread of the spectrum.

Concept: dispersion = refraction with n depending on wavelength. Refraction bends light because speed changes in a medium, and dispersion adds that the speed change depends on wavelength. This is why different colours separate in prisms and droplets.