^Image formation by a lens

(a) A concave lens always form virtual, erect & diminished image irrespective of the position of the object.

(b) With a convex lens following possibilities are there

Position of object	Ray diagram	Image produced
At ∞		At F Real (inverted) Extremely Diminished m < < 1
Beyond C i.e. Between ∞ and 2 F		Between F & C Real (inverted) Diminished m < 1
At C		At C Real (inverted) Same as size of object m = 1
Between F and C		Beyond C Real (inverted) Magnified
Object at F		At ∞ Real (inverted) Infinite size m → ∞
Between F and P		Beyond 2 F Virtual (erect) Magnified m > 1

^Curved surface refraction formula

It is a general expression, applicable to both convex & concave surface, for both point & extended object placed in any medium rare or denser, for any type of image formed (real or virtual).

While using this result keep in mind following points:

1. All distance are measured from the pole P (i.e. the centre of surface at which incident ray strikes.
2. μ₁ → Medium from which incident ray comes.
3. μ₂ → Medium towards which incident ray is sent.

^δ without θ

Under this condition

This combination is also called Achromatic prism combination.

^Dispersive power

It is independent of A but depends upon nature μ_material.

From a single prism it is not possible to get deviation without dispersion, or to get dispersion without deviation, however the two or more be combined in such a way that a white ray of light it may undergo:

(a) Dispersion without deviation (i.e. θ without δ)

(b) Deviation without dispersion (i.e. δ without θ)

^Small angle deviation

δ = A (μ – 1)

δ depends on i, A, μ_prism, μ_medium,

The cause of dispersion is that the speeds of different colours of light in a transparent medium are different.

Also as μ_v > μ_r thus δ_v > δ_r   i.e. the angles of deviation for different colours are different. It is maximum for violet & is minimum for red colour.