To determine the focal length of a convex mirror, we employ the formula:

In this formula, $f$ represents the focal length, $u$ denotes the object distance, and $v$ signifies the image distance.

Experimental Setup

To measure the focal length, follow these steps:

1. Position a Light Source: Place a light source at a known distance from the convex mirror. This distance is referred to as the object distance, denoted by $u$.

2. Set Up a Screen: Position a screen at a certain distance from the mirror. This distance is called the image distance, represented by $v$.

3. Adjust for Clarity: Move the screen closer to or farther from the mirror until a clear image is visible on the screen.

Calculation of Focal Length

Once you have accurately measured both the object distance $u$ and the image distance $v$, you can calculate the focal length using the mirror equation mentioned earlier:

Important Considerations

It is crucial to remember that the focal length of a convex mirror is always negative. This is due to the nature of convex mirrors, which diverge light rays rather than converging them at a focal point. Therefore, when recording the focal length, be sure to include a negative sign.

Conclusion

In summary, measuring the focal length of a convex mirror involves setting up an experiment to accurately determine the object and image distances, followed by using the mirror equation to compute the focal length. This process provides valuable insights into the properties of convex mirrors and their optical behavior.