Appeared in: 2024 (3 sets)
Assertion (A) : Although the surfaces of a goggle lens are curved, it does not have any power.
Reason (R) : In case of goggles, both the curved surfaces are curved on the same side and have equal radii of curvature.
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Official Evaluation Steps & EL10 Insight
Step 1 (Formula / Governing Law & Given Data): [0.5 Mark]
According to the Lens Maker's Formula, the power $P$ of a thin lens in air is given by:
$$P = \frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)$$where:
- $\mu$ is the refractive index of the material of the lens with respect to air.
- $f$ is the focal length of the lens.
- $R_1$ and $R_2$ are the radii of curvature of the two surfaces.
Step 2 (Step-by-Step Mathematical Working): [0.25 Mark]
For a goggle lens, both surfaces are curved on the same side (convex-concave shell with uniform thickness) and have equal radii of curvature.
Using the Cartesian sign convention, both centres of curvature lie on the same side of the lens: