Question

Assertion: Although the surface of the goggles is curved, it does not have any optical power.
Reason: In the case of goggles, both the curved surfaces have equal radii of curvature and have center of curvature on the same side.
A) Both assertion and reason are correct and the reason is the correct explanation for the assertion.
B) Both assertion and reason are correct but the reason is not the correct explanation for the assertion.
C) Assertion is correct but the reason is not correct.
D) Both assertion and reason are not correct.

Answer 1

Recall that the power of a curved surface is the inverse of the focal length. So if the focal length increases, then power will increase. But the surface of goggles’ has no optical power. This means that their focal length might be zero.

Complete step by step answer:
Step I:
In the case of lenses, their shape is such that both the surfaces are in the opposite direction. Hence the ray of light passing through them will undergo refraction once it strikes the surface of the lens. The light rays will either converge or diverge at a point.
Step II:
But in the case of goggles’, both the lenses: convex lens and concave lens are used to form the surface of the goggle. The outer curved surface of the goggles’ is in the shape of a convex lens and the inner curved surface is in the shape of a concave lens. But both the surfaces have the same radius of curvature.
Step III:
Because of the same radius of curvature, the light rays passing through both the surfaces will not converge or diverge. They will remain parallel. Hence no focal point and focal length will be there. Since focal length is related to power, so if the focal length is zero, then there will be no power.

Therefore Option (A) is the correct answer.

Note:
It is to be noted that the distance from the pole to the focal point is known as its focal length. The focal length of a lens is half of its radius of curvature. Hence, the focal length increases with an increase in the radius of curvature and vice versa.