Question

Topic : Lenses

Write all formulae used in lenses chap from below topic.

- Lens formula and magnification
-Lens makers formula
-Thin lenses in contact
-Two thin lenses seperated by a distance in air
-Cutting of lenses
-Silvering of lenses
-Lens displacement method !

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Answer 1

Lens Makers Formula

What is the lens makers formula?

Real lenses have the finite thickness between their two surfaces of curvature. An ideal thin lens with two surfaces of equal curvature will have zero optical power. It means it will neither converge nor diverge light. A lens with some thickness which is not negligible is called a thick lens.

Lenses are of two types based on the curvature of the two optical surfaces. Convex and concave.

Lens maker’s formula is the relation between the focal length of a lens to the refractive index of its material and the radii of curvature of its two surfaces. It is used by lens manufacturers to make the lenses of particular power from the glass of a given refractive index.

The lens is thin, therefore the distance measured from the poles of the two surfaces of the lens can be taken to be equal to the distances measured from the optical center.

Formula

Lens maker formula is used to construct a lens with the specified focal length. A lens has two curved surfaces, but these are not exactly the same. If we know the refractive index and the radius of the curvature of both the surface, then we can determine the focal length of the lens by using the given lens maker’s formula:

\(\frac{1}{f}=(\mu-1)\times(\frac{1}{R_1}-\frac{1}{R_2})\)

Where,

f -The focal length of the lens

μ-Refractive index

\(R_1 and R_2\)the radius of the curvature of both surfaces

It is noteworthy that the lens should be thin so that the separation between the two refracting surfaces should be small. Also, the medium on either side of the lens should be the same.

Answer 2

Explanation:

QUESTION :-

LENSES

ANSWER :-

SPHERICAL LENS :- A transparent medium bound by two surfaces , of which one or both surfaces are curved.

There are two types of spherical lenses :-

▪️Convex lens :- Thin form corners

Thick at center

Converging

▪️Concave lens :- Thick from corners

Thin at centre

Diverging

Thin lens formula or lens formula :-

1 1 1

-- = --- + ---

f v u

This equation holds for convex and concave lenses both , but proper signs of u, v and f are to be used according to sign convention of coordinate geometry.

Magnification produced by lens :-

m = I v f

-- = -- -------

O u u + f

where,

I ➡️ size of image

O ➡️ size of object

Lens Maker's formula :-

if R1 and R2 are the radii of curvature of first and second refracting surfaces of a thin lens of focal length ,f then lens Maker's formula is :-

1

--- = ( 1n2 - 1) [ 1/ R1 - 1/ R2]

f

= (n - 1 ) [ 1 / R1 - 1/ R2 ]

where ,

1n2 = n is refractive index of material of lens with respect to surrounding medium.

Thin Lenses In Contact :-

If two or more lenses of focal length f1 , f2 are placed in contact , then their equivalent

focal length F is given by

1 1 1 1

-- = --- + --- + ------- = ---

F f1 f2 f

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