Lenses

Any transparent medium with a curved edge or surface is a lens. There are two types of lenses

i) Converging - lenses are generally thicker at the center than at the ends and they cause rays of light to converge or come together at a point

ii) Diverging - lenses are generally thicker at the edges than at the center and they cause rays of light to diverge or spread out from a point

The principal axis is an imaginary line drawn through the center of curvatures of the lens.

The optical center is the point on the principal axis, mid-way between the center of curvatures of the lens. Rays passing through the optical center are not deviated.

The principal focus, F, of a converging lens is the point to which all incident rays that are parallel to the principal axis converge after refraction by the lens.

The principal focus, F, of a diverging lens is the point from which all incident rays that are parallel to the principal axis appear to diverge from after refraction by the lens

The focal length, f, of a lens is the distance between its optical center and principal focus.

Ray Diagrams

Converging Lenses

Any two of the following rays can be used to locate the image formed when an object is placed in front a lens.

i) A ray parallel to the principal axis passes through the focal point

ii) A ray through the optical center is undeviated

iii) A ray through F` (F prime) emerges parallel to the principal axis.

The image is formed where the two rays meet.

Diverging Lenses

i) Any ray travelling parallel to the principal axis will be refracted away from the principal axis, and will appear to have passed through the focal point when traced back

ii) Any ray heading toward the focal point on the other side of the lens will be refracted and travel parallel to the principal axis after passing through the lens.

iii) Any ray passing through the centre of the lens will be undeviated.

Characteristics of the image formed

The image formed can either be i)inverted or upright, ii) magnified or diminished iii) real or virtual iv) a specified distance from the lens v) on a particular side of the lens.

The position of the image depends on the focal length and the distance of the object from the lens.

Distinguishing Real from Virtual Images

Linear Magnification

The linear magnification of an object by a lens is defined as

height /size of image

m =__________________

height / size of object