Focal Length and Power of Convex Lenses

Introduction:
Convex lenses are optical devices that converge light rays towards a focal point. The focal length of a lens is the distance between the lens and its focal point. The power of a lens is a measure of its ability to converge or diverge light and is defined as the reciprocal of the focal length.

Explanation:
To determine which lens has the greatest power among lenses P, Q, R, and S, we need to compare their respective focal lengths.

Focal Length:
The focal length of lens P is 20cm.
The focal length of lens Q is 15cm.
The focal length of lens R is 5cm.
The focal length of lens S is 10cm.

Power:
The power of a lens is calculated using the formula:
Power (P) = 1 / Focal Length (f)

Let's calculate the power of each lens using this formula.

The power of lens P = 1 / 20 = 0.05 diopters.
The power of lens Q = 1 / 15 = 0.067 diopters.
The power of lens R = 1 / 5 = 0.2 diopters.
The power of lens S = 1 / 10 = 0.1 diopters.

Comparison and Conclusion:
From the calculations, we can see that lens R has the greatest power with a value of 0.2 diopters. This means that lens R has the highest ability to converge or diverge light compared to lenses P, Q, and S.

Therefore, among lenses P, Q, R, and S, lens R has the greatest power due to its smaller focal length of 5cm.