Sign convention for spherical lenses
Sign convention for spherical lenses
Sign convention of spherical lens is similar to the sign
convention of the spherical mirrors.
Object is placed on the left of the lens. It means to say
that light must passes through the lens from left to light.
All measurements of distance are taken from the optical
centre of the lens.
The focal length of a convex lens is positive. And the
focal length of the concave lens is negative.
All distance measured above the principal axis are positive.
All distance measured below the principal axis are negative.
All the distance measured in the direction of incident rays
are positive.
All the distance measured in the direction opposite to that
of the incident rays are negative.
Lens formula and magnification
Lens formula provides the relationship between object
distance (u) , image distance (v) and
the focal length (f). lens formula is applicable of both concave lens and
convex lens.
The image generated by the lens may be real, virtual or of
different sizes. And they depend on the object distance from the lens.
Object distance (u):--
The measurements
of distance of the object from the optical center of the lens is known as
object distance. It is represented by the letter u.
Image distance (v) :--
The measurements
of distance of the image from the optical center of the lens is known as object
distance. It is represented by the letter v.
Focal length of lens:--
The distance of the
principal focus from the optical center of the lens is known as focal length. It
is represented by the letter f.
Lens formula is expressed as :--
1/v -
1/u = 1/f
If the lens equation give the negative image distance , so
the image distance formed is virtual and on the same side as the object.
If the lens formula gives a negative focal length then the
lens is diverging.
Magnification of lens
The magnification of lens is defined as the ration of the
height of image to the ratio of the object.
Magnification of lens is represented by the letter m.
Height of the object is h
Height of the image is h’
Height of the image h’
m = …………………………… =
………..
Height of the object h
Magnification of lens is also related with object distance
(u) and image distance (v).
h’ v
Magnification (m) =…………… = ………….
h u
point to noted:-- if
magnification (m) is positive. Then the image formed is virtual and erect.
if magnification (m) is negative.
Then the image formed is real and inverted.
power of lens:--
power of lens is expressed as the degree of the convergence or divergence of
light rays which is achieved by the lens.
The power of lens is the ability of the lens to converge or
diverge the rays of light depends on its focal length.
Power of lens is expressed as the reciprocal of the focal length.
It is represented by the letter P.
Power of lens is expressed as :--
P = 1/f
The SI unit of power of lens is diopter.
It is denoted by the letter D.
If the focal length of lens (f) is expressed in meters then the power of lens
is expressed in diopters.
1 diopters:--
One diopter
is the power of lens whose focal length is one meter.
1D == 1m-1
.
It is noted that in
the concave lens , power of lens is negative.
It is noted that in
the convex lens , power of lens is positive.
If the lens produces more converging or more diverging ,
then it is said that it has more power.
If the focal length is shorter then the power of lens is more.
It is noted that,
opticians prescribe corrective lens indicating powers.
The lens prescribed has the power equal to +2.0 D.
This means the lens prescribed is convex.
The focal length of the lens is + 0.05 m .
A lens of power -2.5
D has a focal length of -0.40 D. the lens is concave lens.
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