Physics LENS FORMULA

Lens

A lens is an optical system bounded by two or more than two refracting surfaces having common axis.

In simple lens if the surfaces are very close to each other then the lens is called simple thin lens if they are separated by non negligible distance then called simple thick lens.

Thin lens is classified (Geometrically) to following categories.
`=>` Biconvex
`=>` Plane convex
`=>` Biconcave
`=>` Plano concave
`=>` Convexo concave

But according to its action a lens may be of two types.

(i) `text(Converging lens or convex lens)` (If it converges Parallel beam)
(ii) `text(Diverging lens or concave lens)` (If it diverges parallel beam)

`text(Some basic terms related to thin spherical lens :)`

`text(Optic Centre (C) ) :` If a light my is incident on lens is such that after refraction from lens the emergent ray is parallel to the incident ray then the point at which refracted ray intersects the principal axis is called optic centre of that lens.

`text(Primary Focal Point)` (`F_1`) `:` The position of object if image is at infinity is called primary focal point.

Secondary Focal Point (`F_2`) `:` The position of image if object is at infinity is called secondary focal point.

`text(Focal Length)` (`f`) `:` The distance between optical centre and secondary focal point is termed as focal length.

Lens Formula

Consider a thin spherical lens (`m=m_1`) is placed in a medium (`m=m_m`) as shown in figure. Let a point object O is placed on the principal axis of the lens. For the first refracting surface O is an object point and the corresponding image point it `I_1`. Now `I_1` will act as object point for second surface which again form an image at `I`. For lens we can say that O is object point and `I` is image point.

At first surface,

`(mu_1)/(v^')-(mu_m)/u=(mu_1 - mu_m)/R_1......(1)`

At second surface,

`(mu_m)/(v)-(mu_1)/(v^')=(mu_m - mu_1)/R_2......(2)`

Combining (i) and (ii) we get,

`1/v -1/u = ((mu_1)/(mu_2) -1)(1/R_1 - 1/R_2)......(3)`

If `u=oo` `=>` `v=f`

`1/f=((mu_1)/(mu_m) -1)(1/R_1 -1/R_2).......(4)`

This formula is known as `text(lens maker formula)`.

from (3) and (4)

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

This formula is known as `text(lens formula)`.

 
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