The convex lens is mounted L is mounted in front of the convex mirror `MM^'` on an optical bench in such a way that the principal axes of lens and mirror coincide. An object pin is placed in front of the lens in such a way that the tip O of the pin lies on the common principle axis fig (a) Light rays from O, after refraction through the lens, fall on the mirror. After reflection from the mirror, the rays pass again through the lens and from a real image `I` towards O. Now, the object-pin is moved back and forth in front the lens and adjusted in a position in which there is no parallax between the pin and its image. In this position, the ray after passing through the lens fall normally on the mirror and hence retrace their path to form the image `I` at the same position as the object O. The position of the mirror `MM^'` is read on the optical bench.
Now, keeping the object pin and the lens fixed on the bench, the mirror is removed. Since, the rays emerging from the lens were falling normally on the mirror, it means that they were converging towards the centre of curvature C of the mirror. Hence, after removing the mirror, the rays will meet at C (fig. b), where the real image `I^'` of O will be formed by the lens located by adjusting the position of an image-pin such that the image `I` and the image-pin are mutually non-parallax. The difference between the positions of the mirror and the image-pin is the radius of curvature R of the mirror.
The focal length of mirror is `R/2`.
The convex lens is mounted L is mounted in front of the convex mirror `MM^'` on an optical bench in such a way that the principal axes of lens and mirror coincide. An object pin is placed in front of the lens in such a way that the tip O of the pin lies on the common principle axis fig (a) Light rays from O, after refraction through the lens, fall on the mirror. After reflection from the mirror, the rays pass again through the lens and from a real image `I` towards O. Now, the object-pin is moved back and forth in front the lens and adjusted in a position in which there is no parallax between the pin and its image. In this position, the ray after passing through the lens fall normally on the mirror and hence retrace their path to form the image `I` at the same position as the object O. The position of the mirror `MM^'` is read on the optical bench.
Now, keeping the object pin and the lens fixed on the bench, the mirror is removed. Since, the rays emerging from the lens were falling normally on the mirror, it means that they were converging towards the centre of curvature C of the mirror. Hence, after removing the mirror, the rays will meet at C (fig. b), where the real image `I^'` of O will be formed by the lens located by adjusting the position of an image-pin such that the image `I` and the image-pin are mutually non-parallax. The difference between the positions of the mirror and the image-pin is the radius of curvature R of the mirror.
The focal length of mirror is `R/2`.
