Lens Formula

The relation between distance of object, distance of image and focal length for a lens is called lens formula.

`1/v-1/u=1/f`

Where, v is the distance of image, u is the distance of object, and f is the focal length of lens. Distance of object and image is measure from the optical centre of the lens. The sign for distance is given as per convention.

The lens formula is valid for all situations for spherical lens. By knowing any of the two the third can be calculated.

Magnification

The ratio of height of image and that of object or ratio of distance of image and distance of object gives magnification. It is generally denoted by ‘m’.

`m=text(Height of image h’)/text(Height of object h)`

`=text(Distance of image v)/text(Distance of object u)`

The positive (+) sign of magnification shows that image is erect and virtual while a negative (-) sign of magnification shows that image is real and inverted.

Power of Lens

A convex lens with short focal length converges the light rays with greater degree nearer to principal focus and a concave lens with short focal length diverges the light rays with greater degree nearer to principal focus.

The degree of divergence or convergence of ray of light by a lens is expressed in terms of the power of lens. Degree of convergence and divergence depends upon the focal length of a lens. The power of a lens is denoted by ‘P’. The power of a lens is reciprocal of the focal length.

`text(Power P)=1/text(Focal length f)`

Or, `P=1/f`

The SI unit of Power of lens is dioptre and it is denoted by ‘D’.

Power of a lens is expressed in dioptre when the focal length is expressed in metre. Thus, a lens having 1 metre of focal length has power equal to 1 dipotre.

Therefore, 1 D = 1 m⁻¹

A convex lens has power in positive and a concave lens has power in negative.

Power of optical instruments having multiple lenses:

If there is more than one lens used, then total power of lenses is equal to the sum of power of all individual lenses.

Example: If there are three lenses used in an optical device having powers equal to 1 D, 2D and 3D respectively,

Therefore, the total power of the optical device `= 1D + 2D + 3D = 6D`

Some common phenomena of Refraction:

1. Bending of pencil when placed in a glass with water: When a pencil or stick is kept in a beaker or a glass filled with water, the stick appears slightly bent. This happens because the light; entering from air (rarer medium) into water (denser medium); bends towards normal to the incident which makes the appearance of pencil or stick as bent.
2. Position of fish in the water of pond: The ray coming from fish in the pond bends away from the normal to the incident. We see the emergent ray which makes the appearance of fish slightly above its position.
3. Formation of rainbow: Rainbow is formed just after the rain. When ray of light travels from droplets of rain, it is scattered into its constituent seven colours and forms a rainbow in the sky.
4. Visibility of sun slightly before the time of sunrise: When the rays coming from the sun enter into atmosphere (which is denser medium than vacuum), they bend away from normal to the incidence because of refraction. Since we see the refracted rays coming from the sun, that’s why the sun becomes visible slightly ahead of the time of sunrise.