Question

Find the focal length of convex mirror using convex lens.

Hint:

The convex lens chosen for this experiment should have a focal length smaller than the radius of curvature of the convex mirror. This ensures that a real image can be formed by the lens at a position that can coincide with the mirror's center of curvature.

Answer 1

Step 1: Understanding the Concept:
A convex mirror always forms a virtual image, which cannot be located directly. This experiment uses a convex lens to first form a real image. This real image then acts as a virtual object for the convex mirror. By adjusting the convex mirror's position, the rays are made to reflect back along their incident path, forming a final image at the same location as the original object. This occurs when the rays incident on the convex mirror are directed towards its center of curvature.
Step 2: Key Formula and Apparatus:
Apparatus Required:
An optical bench, a convex mirror, a convex lens, a mirror holder, a lens holder, an optical needle (object pin), and a meter scale.
Key Formula:
The focal length (f) of a spherical mirror is half its radius of curvature (R). \[ f = \frac{R}{2} \] Step 3: Detailed Procedure:
1. Setup without Mirror: Mount the convex lens on the optical bench. Place an object pin (O) in front of the lens. Adjust its position to form a clear, real, and inverted image (I) on the other side. Note the position of the image I by using another needle and removing parallax.
2. Introducing the Mirror: Place the convex mirror on a holder and position it between the convex lens and the image position I. The reflecting surface of the mirror should face the lens.
3. Retracing Path: Adjust the position of the convex mirror along the optical bench until the light rays, after reflecting from the mirror, retrace their path back through the lens and form a final image at the same position as the original object pin O. This is confirmed by removing the parallax between the object pin and its image.
4. Locating Center of Curvature: In this adjusted position, the light rays from the lens are incident normally on the convex mirror. This means they are converging towards the center of curvature (C) of the mirror. Thus, the position of the image I (found in step 1) is the location of the center of curvature C of the mirror.
5. Measurement: Record the position of the convex mirror. The distance between the pole of the convex mirror and the position of image I is the radius of curvature (R).
Step 4: Calculation:
Calculate the focal length of the convex mirror using the measured radius of curvature R. \[ f = \frac{R}{2} \] Repeat the experiment two to three times for different object positions and find the mean focal length.