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 relationship given in the question:

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

2. **Identifying the Dimension of Focal Length**: The focal length \( f \) is a measure of distance. Therefore, its dimension can be expressed as:
\[ [f] = L \]
where \( L \) represents the dimension of length.

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

4. **Conclusion**: The dimensions of the power of a lens are:
\[ [P] = L^{-1} \]

Thus, the final answer is that the dimensions of the power of a lens is \( L^{-1} \).

---