By Plotting `(1)/(v)` verus `(1)/(u)` focal length of a convex mirror can be found .

Options

A. No as it forms a virtual image
B. Yes only if scale is large
C. Yes only if scale is small
D. Yes only if aperture is small

Answer

To determine the focal length of a convex mirror by plotting \( \frac{1}{v} \) versus \( \frac{1}{u} \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Mirror Formula**: The mirror formula for a convex mirror is given by:
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]
where:
- \( f \) is the focal length,
- \( v \) is the image distance (always negative for a convex mirror),
- \( u \) is the object distance (always negative as per the sign convention).

2. **Set Up the Experiment**: Place an object at various distances from the convex mirror. Measure the corresponding image distances using a screen or a measuring device.

3. **Record Data**: For each position of the object, record the values of \( u \) (object distance) and \( v \) (image distance). Remember to take the negative values for both distances as per the sign convention.

4. **Calculate \( \frac{1}{u} \) and \( \frac{1}{v} \)**: For each pair of \( u \) and \( v \) values, calculate \( \frac{1}{u} \) and \( \frac{1}{v} \).

5. **Plot the Graph**: Create a graph with \( \frac{1}{v} \) on the y-axis and \( \frac{1}{u} \) on the x-axis.

6. **Analyze the Graph**: The graph should yield a straight line. The slope of this line can be used to find the focal length.

7. **Determine the Focal Length**: From the linear equation derived from the graph, you can rearrange it to find \( f \). The intercept of the graph can also help in determining the focal length.

### Conclusion:
From the graph of \( \frac{1}{v} \) versus \( \frac{1}{u} \), we can analyze the relationship and determine the focal length of the convex mirror. However, it is important to note that the image formed by a convex mirror is virtual and erect, which affects the interpretation of the results.