The correct option is m = v/u.
Explanation
Linear magnification ($m$) produced by a spherical lens is defined as the ratio of the height of the image ($h'$) to the height of the object ($h$). It indicates the extent to which the image is larger or smaller relative to the object.
Detailed Analysis
- For Spherical Lenses: The magnification is related to the object distance ($u$) and image distance ($v$) by the formula:
$m = \frac{v}{u}$
Here, distances are measured from the optical center of the lens. The sign convention dictates that distances measured in the direction of incident light are positive, and those opposite are negative. - Comparison with Mirrors: It is crucial to distinguish this from spherical mirrors, where the magnification formula is $m = -\frac{v}{u}$. The negative sign appears in the mirror formula due to the reflection convention, whereas the lens formula (based on refraction) carries a positive sign for the ratio of distances.
Key Takeaway
Magnification Formulae:
- Lens: $m = \frac{v}{u}$
- Mirror: $m = -\frac{v}{u}$