Which method is more accurate in the determination of `f` for a concave mirror.
(i) `u` versus `v` or
(ii) `(1)/(u)` versus `(1)/(v)` graphs ?

Explanation

To determine which method is more accurate for finding the focal length \( f \) of a concave mirror, we will analyze two different graphical methods: (i) the \( u \) versus \( v \) graph and (ii) the \( \frac{1}{u} \) versus \( \frac{1}{v} \) graph.

### Step-by-Step Solution:

1. **Understanding the Relationships**:
- For a concave mirror, the mirror formula is given by:
\[ \frac{1}{f} = \frac{1}{u} + \frac{1}{v} \]
- Here, \( u \) is the object distance (measured from the mirror), and \( v \) is the image distance.

2. **Graphing \( u \) versus \( v \)**:
- When plotting \( v \) against \( u \), the relationship is hyperbolic. This means that as \( u \) increases, \( v \) approaches zero and vice versa.
- The graph does not yield a straight line, making it difficult to extract precise values for \( f \).

3. **Graphing \( \frac{1}{u} \) versus \( \frac{1}{v} \)**:
- Rearranging the mirror formula gives:
\[ \frac{1}{v} = -\frac{1}{u} + \frac{1}{f} \]
- This equation represents a linear relationship, where plotting \( \frac{1}{v} \) against \( \frac{1}{u} \) produces a straight line.
- The y-intercept of this line will be \( \frac{1}{f} \), making it straightforward to determine the focal length.

4. **Comparing Accuracy**:
- The hyperbolic graph (from the \( u \) versus \( v \) method) makes it challenging to accurately determine the values of \( u \) and \( v \) due to the non-linear nature of the graph.
- In contrast, the linear graph (from the \( \frac{1}{u} \) versus \( \frac{1}{v} \) method) allows for easier calculations and more accurate determination of the focal length \( f \).

5. **Conclusion**:
- The method using the graph of \( \frac{1}{u} \) versus \( \frac{1}{v} \) is more accurate for determining the focal length \( f \) of a concave mirror compared to the \( u \) versus \( v \) graph.