## Mirror and lens

### Concave mirror and Convex mirror

A concave mirror reflects light from sunken side and a convex mirror reflects light from the surface which is bulged out. In both the mirrors, f = R/2 and i/f = 1/v+1/u, Where u = distance of object from the pole of mirror, v = distance of image from pole of mirror, f =principle focal length of mirror = distance of principal focus F from pole P. R= radius of curvature of mirror = distance of centre of curvature C from pole P. The new Cartesian sign conventions are:

1) All distances are measured from pole of mirror,
2) The distance measured in the direction of incidence of light is taken as positive and vice-versa. For a convex mirror, f and R are positive. For a concave mirror, f and R are negative.

### Lens

A lens is a piece of transparent refracting material, which is bounded by two spherical surfaces or by one spherical surface and one plane surface. Two main types of lenses are:
1) Convex lens or converging lens, which is think at the middle and thin at the edges.
2) Concave lens or Diverging lens, which is think at the edges, and thin at the centre

### Lens maker’s formula

Lens maker formula is 1/f= (µ-1)(1/R1-1/R2) As per new Cartesian sign convention, For a convex lens, R1 is positive; R2 is negative For a concave lens, R1 is negative; R2 is positive In this formula, µ is refractive index of the material of the lens with respect to the surrounding medium. In general, if µ2 is refractive index of the material and µ1 is refractive index of the medium in which the lens is placed. Then µ = µ2 / µ1. Note that if µ1> µ2, focal length (f) of convex lens becomes negative. It means a convex lens would behave as a concave lens, when placed in a medium of refractive index greater than that of the lens material. The reverse is also true.

### Power of a lens

Power of a lens = i/f When f =1m, P= a dioptre (D). For a convex lens, P is positive. For a concave lens, P is negative.

### The Spectrometer

A spectrometer is used for obtaining pure spectrum of a source o flight and measuring refractive index (µ) of material of prism and (µ) of a transparent liquid. A spectrometer consists of three parts:
1) Collimator that provides a parallel beam of light
2) Prism Table for holding the prism
3) Telescope for observation and measurements. We set first the telescope for parallel rays, then the collimator for parallel rays and finally the prism in the minimum deviation position, to observe a pure spectrum Measure dm and A, and use prism with very thin glass walls. Note that in a pure spectrum, there is no overlapping of colours i.e. different colours occupies their own distinct position. The spectrum in which different colours overlap is called an impure spectrum.

### Fraunhoffer lines

Fraunhoffer lines are a few dark lines observed in the otherwise continuous spectrum of the sun. Their existence was explained by Fraunhoffer on the basis of Kirchhoff’s law.

### Colour of sky

Blue colour of sky is due to scattering of light (Is ∝ 1/ λ4) . Clouds are at much lower heights. They are seen by light scattered from dust particle which is same for all colours. Therefore, clouds look white. Sun appears red at sunrise and sunset because red colour is least scattered.

### Rainbow

Rainbow is a beautiful arc of seven colours seen in the sky after rainfall. This is formed due to dispersion of sunlight from rain drops suspended in air after rain fall. To observe the rainbow, back of observer must be towards the sun. The primary rainbow is much brighter compared to the secondary rainbow. Note that in primary rainbow, lower arc is violet and upper arc is red. In secondary rainbow, lower arc is red and upper arc is violet.