AIIMS 2007 Physics Lens Power Assertion Reason Question

To analyze the given assertion and reason concerning the power of goggles, we need to delve into the concepts of lens power and the characteristics of lenses.

Assertion: Goggles have zero power.

Explanation: The power $P$ of a lens is defined as the reciprocal of its focal length $f$ in meters:

$$P = \frac{1}{f}$$

A lens has positive power if it converges light (convex lens) and negative power if it diverges light (concave lens). For a lens to have zero power, its focal length must approach infinity. In practical terms, this means that a lens is neutral and does not converge or diverge light, which is characteristic of goggles that are designed to provide protection rather than optical correction.

Reason: Radius of curvature of both sides of the lens is the same.

Explanation: The radius of curvature of a lens is related to its shape and affects its focal length. For a lens with equal radii of curvature on both sides, it is symmetrical, but this does not necessarily mean it has zero power. The power of a lens is also influenced by the refractive index of the material and the lens's overall geometry.

If both radii of curvature are the same but the lens is made of a material with a significant refractive index, it could still have non-zero power. Therefore, the reason provided does not accurately explain why goggles, specifically, have zero power.

Analysis of Options:

• A) If both assertion and reason are true and reason is the correct explanation of assertion.

  • This is incorrect because while the assertion about goggles having zero power is true, the reason does not correctly explain the assertion.

• B) If both assertion and reason are true but reason is not the correct explanation of assertion.

  • This is the correct option. The assertion is true (goggles have zero power), but the reason (equal radii of curvature) does not provide a correct explanation for it.

• C) If assertion is true but reason is false.

  • This option is incorrect because while the assertion is true, the reason itself is not false; it is simply not an explanation for the assertion.

• D) If both assertion and reason are false.

  • This option is incorrect because the assertion is true.

Conclusion:

The correct answer is B: both the assertion and reason are true, but the reason does not adequately explain the assertion regarding the power of goggles. This distinction is crucial in understanding the relationship between the physical properties of lenses and their optical functions.