If ‘u’ is the object-distance, ‘v’ is the image-distance and ‘f’ is the focal length of a spherical mirror then which of the following is a correct expression for the mirror formula?

1/v + 1/u = 1/f

The correct answer is option 3. \(\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\).

The mirror formula is a fundamental equation in optics that relates the object distance (\(u\)), image distance (\(v\)), and focal length (\(f\)) of a spherical mirror. It is derived from the geometry of light rays reflected by a spherical mirror.

The correct expression for the mirror formula is:

\[ \frac{1}{v} + \frac{1}{u} = \frac{1}{f} \]

Where:

\(u\) is the object distance, the distance between the object and the mirror.

\(v\) is the image distance, the distance between the image and the mirror.

\(f\) is the focal length of the mirror.

The equation states that the reciprocal of the object distance plus the reciprocal of the image distance is equal to the reciprocal of the focal length. This equation holds true for both concave and convex spherical mirrors.

Explanation:

When the object is located beyond the focal point (\(u > f\)), the image distance (\(v\)) is positive, and the image is real and inverted.

When the object is located at the focal point (\(u = f\)), the image distance (\(v\)) approaches infinity, and the image is formed at infinity.

When the object is located between the focal point and the mirror (\(0 < u < f\)), the image distance (\(v\)) is negative, and the image is virtual and upright.

When the object is located at the mirror (\(u = 0\)), the image distance (\(v\)) is equal to the focal length (\(v = f\)).

In summary, the mirror formula quantifies the relationship between the object, image, and focal length of a spherical mirror, enabling the determination of image characteristics based on object position and mirror properties.