In the experiment to determine the focal length of a concave mirror by graphical methods the u - v graph is

Options

A. A straight line
B. A circle
C. An ellipse
D. None of these

Answer

To determine the focal length of a concave mirror using the u-v graph, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Mirror Formula**:
The mirror formula for a concave mirror is given by:
\[ \frac{1}{f} = \frac{1}{u} + \frac{1}{v} \]
where \( f \) is the focal length, \( u \) is the object distance (taken as negative for concave mirrors), and \( v \) is the image distance (also negative for real images).

2. **Rearranging the Formula**:
We can rearrange the mirror formula to express \( v \) in terms of \( u \):
\[ v = \frac{fu}{u + f} \]
This shows that \( v \) depends on \( u \) and \( f \).

3. **Graphing the Relationship**:
When plotting the u-v graph:
- The x-axis represents the object distance \( u \).
- The y-axis represents the image distance \( v \).
- Since both \( u \) and \( v \) are negative for real images formed by a concave mirror, the graph will be in the second quadrant.

4. **Analyzing the Graph**:
The relationship between \( u \) and \( v \) is not linear. Instead, it will show a hyperbolic nature because as \( u \) approaches the focal point, \( v \) approaches infinity, and vice versa.

5. **Conclusion**:
Based on the characteristics of the graph, we conclude that the u-v graph for a concave mirror is neither a straight line nor a circle or ellipse. Therefore, the correct answer is that the u-v graph is none of the above options.

### Final Answer:
The u-v graph for a concave mirror is none of the given options.

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