Correct Option
The correct option is Both A and R are true and R is the correct explanation of A
Explanation
The power of a lens ($P$) is a measure of its ability to converge or diverge light rays. It is mathematically defined as the reciprocal of the focal length ($f$) measured in meters. The formula is given by $P = \frac{1}{f}$. The sign of the power is directly determined by the sign of the focal length, based on the standard Cartesian sign convention.
Statement-wise Analysis
- Assertion (A): Correct. A convex lens acts as a converging lens. By convention, the power of a converging lens is taken as positive.
- Reason (R): Correct. The principal focus of a convex lens is real and lies on the side opposite to the incident light. According to the sign convention, the focal length ($f$) of a convex lens is positive. Since power is defined as the reciprocal of focal length ($P = \frac{1}{f}$), a positive denominator ($f$) results in a positive value for power ($P$).
Conclusion: The reason provides the fundamental definition ($P = \frac{1}{f}$) and the specific property of the convex lens (positive focal length) that necessitates the assertion. Thus, R is the correct explanation of A.
Key Takeaway: Power is the reciprocal of focal length ($P = \frac{1}{f}$). For a convex lens, focal length is positive, resulting in positive power. For a concave lens, focal length is negative, resulting in negative power.