Question

The dimensional formula for the power of a lens is

• A. [L^-1M⁰T⁰]
• B. [L⁰M^-1T⁰]
• C. [L⁰M^-1T⁰]
• D. [L^-1M⁰T⁰]
• E. [L^-1M⁰T^-1]

Answer 1

The Correct Option is A

The power \( P \) of a lens is defined as the reciprocal of its focal length. The dimensional formula for the power of a lens is the same as that of the inverse of length, which is \( [L^{-1}] \). Since power involves only the length dimension, the mass \( M \) and time \( T \) have exponents of 0.
Hence, the dimensional formula for the power of a lens is \( [L^{-1} M^0 T^{0}] \).

The correct option is (A) : \([L^{-1} M^0 T^{0}]\)

Answer 2

The power of a lens is defined as the reciprocal of the focal length (in meters). That is: 

$P = \frac{1}{f}$  

The dimensional formula for focal length is $[L]$. Hence, the dimensional formula for power is: 

$[L^{-1}]$ 

Since it has no dependence on mass or time, the complete dimensional formula becomes: 

Correct answer: [L^-1M⁰T⁰]