Goggle Lens Power – Rankers Physics

Refraction by Spherical Surfaces: Practice Problem & Solution

Assertion (A): Although the surface of goggles lens are curved, it does not have any power. Reason (R): In case of goggles, both the curved surfaces have equal radius of curvature and have centre of curvature on the same side  
(1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
(2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(3) (A) is true but (R) is false
(4) Both (A) and (R) are false

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Refraction by Spherical Surfaces. Understanding the underlying formula is key to arriving at the correct answer below:

Protective goggle lenses do not alter vision, implying their optical power is zero. Thus, (A) is true.
The power of a lens is given by \(P = (n-1)(\frac{1}{R_1} - \frac{1}{R_2})\). If the surfaces have equal radii of curvature and their centers are on the same side (as in a meniscus lens where both surfaces curve in the same direction), then \(\frac{1}{R_1} - \frac{1}{R_2} = 0\), resulting in (P = 0). This explains why curved goggle lenses can have no power. Thus, (R) is true and is the correct explanation of (A).

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