Dispersion in optics: Select the correct combined statements about refractive index variation and the prism spectrum
-
AThe refractive index of a medium varies with the radiation’s wavelength
-
BThe wavelength dependence of refractive index is called dispersion
-
CA prism splits white light into colors because of dispersion
-
DAll of the above
-
ENone of the above
Answer
Correct Answer: All of the above
Explanation
Introduction / Context:Dispersion—variation of refractive index with wavelength—underlies many optical effects, from chromatic aberration in lenses to the rainbow spectrum produced by prisms. This question asks you to recognize the standard definitions and the causal link between dispersion and color separation.
Given Data / Assumptions:
- White light contains a continuum of wavelengths.
- Most transparent media show normal dispersion (n decreases as wavelength increases in the visible range).
- Prisms refract different wavelengths by different amounts.
Concept / Approach:Because n = n(λ), the angle of refraction depends on λ via Snell’s law. Shorter wavelengths (violet/blue) usually experience higher refractive indices and therefore larger deviations than longer wavelengths (red). This wavelength-dependent bending separates white light into its constituent colors.
Step-by-Step Solution:Confirm statement a: n varies with λ → true for dispersive media.Confirm statement b: the phenomenon is named “dispersion”.Confirm statement c: prism spectrum is a direct consequence of dispersion.Therefore, all three are correct simultaneously.
Verification / Alternative check:Empirical refractometer data show n(λ) curves; ray-tracing through a prism reproduces the color fan consistent with observed spectra.
Why Other Options Are Wrong:Any single choice omits part of the full definition–phenomenon linkage.“None” contradicts standard optics.
Common Pitfalls:Confusing dispersion with diffraction; prisms separate colors by refraction, not by interference from apertures or gratings.
Final Answer:All of the above.