The power of lens is `P=1/(f)` where `f` is focal length of the lens. The dimensions of power of lens is

Options

A. [L]
B. `[ML^(2)T^(-3)]`
C. `[L^(-1)]`
D. `[MLT^(-3)]`

Answer

To find the dimensions of the power of a lens, we start with the formula given:

1. **Understanding the Formula**: The power \( P \) of a lens is defined as:
\[ P = \frac{1}{f} \]
where \( f \) is the focal length of the lens.

2. **Identifying the Dimensions of Focal Length**: The focal length \( f \) is a measure of distance and is typically expressed in meters (m). In terms of dimensions, we can express this as:
\[ [f] = L^1 \cdot M^0 \cdot T^0 \]
Here, \( L \) represents length, \( M \) represents mass, and \( T \) represents time. Since focal length is a distance, it has the dimension of length.

3. **Finding the Dimensions of Power**: Since power \( P \) is the reciprocal of focal length \( f \), we can express the dimensions of power as:
\[ [P] = \frac{1}{[f]} = \frac{1}{L^1} = L^{-1} \]

4. **Final Result**: Therefore, the dimensions of the power of the lens are:
\[ [P] = L^{-1} \]

### Summary:
The dimensions of the power of a lens are \( L^{-1} \).

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