The focal length and magnification of a plane mirror are :

Question

Accepted Answer

The focal length and magnification of a plane mirror are given as Option 2: $ f = \infty, m = 1 $. Let's explore why this is the correct answer and why the other options are incorrect.

### Explanation for Option 2: $ f = \infty, m = 1 $

1. **Focal Length ($ f = \infty $):**
   - A plane mirror is flat and does not converge or diverge light rays. In optical terms, this means it has an infinite focal length. The focal length is defined as the distance from the mirror to the focal point, where parallel rays of light either converge or appear to diverge from. Since a plane mirror does not focus light, its focal point is considered to be at infinity.

2. **Magnification ($ m = 1 $):**
   - Magnification is the ratio of the height of the image to the height of the object. For a plane mirror, the image formed is virtual, upright, and of the same size as the object. Therefore, the magnification is 1, indicating that the image size is equal to the object size.

### Explanation for Why Other Options are Incorrect

1. **Option 1: $ f = \infty, m = \infty $**
   - While the focal length $ f = \infty $ is correct for a plane mirror, the magnification $ m = \infty $ is incorrect. An infinite magnification would imply that the image size is infinitely larger than the object size, which is not the case for a plane mirror. The image is the same size as the object, so the magnification is 1, not infinity.

2. **Option 3: $ f = 0, m = 1 $**
   - This option incorrectly states that the focal length is 0. A focal length of 0 would imply that the mirror is focusing light at its surface, which is not true for a plane mirror. The correct focal length is infinity. The magnification $ m = 1 $ is correct, but the focal length makes this option incorrect.

3. **Option 4: $ f = 0, m = 0 $**
   - Both the focal length and magnification are incorrect in this option. A focal length of 0 is not applicable to a plane mirror, as explained earlier. Additionally, a magnification of 0 would imply that no image is formed, which is incorrect. A plane mirror forms a virtual image with a magnification of 1.

In conclusion, Option 2 is the correct answer because it accurately describes the properties of a plane mirror: an infinite focal length and a magnification of 1.