Correct Option: (ii) Violet light
Step 1 (Formula / Governing Law & Given Data): [0.5 Mark]
The focal length $f$ of a convex lens is given by the Lens Maker's Formula:
$$ \frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) $$Where $\mu$ is the refractive index of the lens material and $R_1, R_2$ are the radii of curvature. From the relation, we observe that:
$$ f \propto \frac{1}{(\mu - 1)} $$According to Cauchy’s dispersion formula, the refractive index $\mu$ is inversely related to the wavelength $\lambda$ ($\mu \propto \frac{1}{\lambda^2}$).
Step 2 (Step-by-Step Mathematical Working): [0.25 Mark]
- The wavelength of light follows the order: $\lambda_{violet} < \lambda_{blue} < \lambda_{yellow} < \lambda_{red}$.
- Since $\mu$ is inversely proportional to $\lambda$, the refractive index follows the order: $\mu_{violet} > \mu_{blue} > \mu_{yellow} > \mu_{red}$.
- Substituting this into the focal length relation: as $\mu$ increases, $(\mu - 1)$ increases, which causes the focal length $f$ to decrease.
- Therefore: $f_{violet} < f_{blue} < f_{yellow} < f_{red}$.
Step 3 (Final Concluded Answer): [0.25 Mark]
Since the focal length $f$ represents the distance from the optical center where parallel rays converge, the light with the smallest focal length converges nearest to the lens. Thus, Violet light converges nearest to the lens.
💡 EL10 Concept Insight: Think of the lens as a prism that bends light; violet light is "lazier" and gets bent much more sharply than red light, so it hits the focal point much sooner after passing through the glass.