1) What is lenses?
Lenses are used in spectacles. They are also used in telescopes .
A lens is a transparent medium bound by two surfaces. The lens which has two spherical surfaces which are puffed up outwards is called a convex or double convex lens.This lens is thicker near the centre as compared to the edges. The lens with both surfaces spherical on the inside is called a concave or double concave lens. This lens is thinner at the centre as compared to its edges.
2) What is Centre of curvature (C) :
The centres of spheres whose parts form surfaces of the lenses are called centres of curvatures of the lenses.
3) What is Radius of curvature (R) :
The radii of the spheres whose parts form surfaces of the lenses are called the radii of curvature of the lens.
4) What is Principal axis :
The imaginary line passing through both centres of curvature is called the principal axis of the lens.
5) What is Optical centre (O) :
The point inside a lens on the principal axis, through which light rays pass without changing their path is called the optical centre of a lens.
6) What is Principal focus (F) :
When light rays parallel to the principal axis are incident on a convex lens, they converge to a point on the principal axis. This point is called the principal focus of the lens.
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Light rays parallel to the principal axis falling on a convex lens come together i.e. get focused at a point on the principal axis. So this type of lens is called a converging lens.
Rays travelling parallel to the principal axis of a concave lens diverge after refraction in such a way that they appear to be coming out of a point on the pricipal axis. This point is called the principal focus of the concave lens.
Light rays parallel to the principal axis falling on a concave lens go away from one another (diverge) after refraction. So this type of lens is called a divergent lens.
7) What is Focal length (f) :
The distance between the optical centre and principal focus of a lens is called its focal length.
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Three rules of a rays diagram
Rule 1: When the incident ray is parallel to the principal axis,the refracted ray passes through the principal focus.
Rule 2: When the incident ray passes through the principal focus, the refracted ray is parallel to the principal axis.
Rule 3: When the incident ray passes through the optical centre of the lens, it passes without changing its direction.
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8) What is Sign convention :
According to the Cartesian sign convention, the optical centre (O) is taken to be the origin. The principle axis is the X-axis of the frame of reference.
The sign convention is as follows.
1. The object is always placed on the left of the lens, All distances parallel to the principal axis are measured from the optical centre (O).
2. The distanced measured to the right of O are taken to be positive while those measured
to the left are taken to be negative.
3. Distances perpendicular to the principal axis and above it are taken to be positive.
4. Distances perpendicular to the principal axis and below it are taken to be negative.
5. The focal length of a convex lens is positive while that of a concave lens is negative.
9) what is Magnification ( M ) :
The magnification due to a lens is the ratio of the height of the image (h2) to the height of the object (h1).
Magnification = Height of the image
-------------------------------
Height of the object
i.e. M = h2
------ .............(1)
h1
The magnification due to a lens is also related to the distance of the object (u) and that of the image (v) from the lens.
Magnification = distance of the image
------------------------------------
distance of the object
i.e. M = v
--- ...........(2)
u
10 ) what is Power of a lens (p) :
The capacity of a lens to converge or diverge incident rays is called its power (P). The power of a lens depends on its focal length. Power is the inverse of its focal length (f); f is expressed in meters.The unit of the power of a lens is Dioptre (D).
P= 1 1 Dioptre = 1
----- -----
f(m) 1 m
Combination of lenses
If two lenses with focal lengths f1 and f2 are kept in contact with each other, the combination has an effective focal length given by
1 1 1
-- = --- + ---
f f1 f2
If the powers of the two lenses are P1 and P2 then the effective power of their combination is P = P1 + P2.Thus, when two lenses are kept touching each other, the power of the combined lens is equal to the sum of their individual powers.
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