Question

Why is that sun-glasses(goggles), which have curved surfaces, do not have any power?

Answer 1

To answer this question, we first need to understand the power of glasses. The component of your prescription labelled 'Power' or 'Sphere' tells how much correction your vision needs to work properly. This is also known as PWR/SPH or just PWR. This will be presented in the form of a number with a minus or plus sign in front of it.

Complete step-by-step solution:
Optical power - The degree to which a lens, mirror, or other optical device converges or diverges light is known as optical power (also known as dioptric power, refractive power, focusing power, or convergence power). It is equal to the reciprocal of the device's focal length: P is equal to 1/f. A small focal length equates to a high optical power. The inverse meter (m-1), often known as the diopter, is the SI unit for optical power.
Diverging lenses have a negative optical power, whereas convergent lenses have a positive optical power. The optical power and focal length of a lens vary when it is immersed in a refractive liquid.
The two surfaces of the goggle lens are parallel, meaning they have the same curvature radii. The powers of the two surfaces are equal but of opposite signs since one is convex and the other is similarly concave. The total power of the goggle lens (p’) is equal to the algebraic sum of the various surfaces' powers.
$p\prime = {p_1} + {p_2} = p + ( - p) = 0$
So, the final answer is that power is zero.

Note: The focal length of an optical system is the inverse of the system's optical power; it measures how strongly the system converges or diverges light. A system with a positive focal length converges light, while one with a negative focal length diverges light. A system with a shorter focal length bends the rays more sharply, bringing them closer to the focus or diverging them faster.