Innovative Pedagogy Development Centre, Shri Shivaji Science College, Amravati

1. P.A. Nagpure
Department of Physics
Shri Shivaji Science College, Amravati
Lenses
(Lecture – I)

2. Lens
Types
 A lens is made up of transparent medium (glass) and is
bounded by two regular curved (spherical) surfaces.
 Lens is an image forming device. It forms an image by
refraction of light at its two bounding surfaces. A single lens
with two refracting surfaces is a simple lens.
 As it is easy to make spherical surfaces, most of the lenses are
made of spherical surfaces and have a wide range of
curvatures.
 Converging (Convex) : One or both surfaces bulged outside.
 Diverging (Concave) : One or both surfaces bulged inside.
P.A. Nagpure

3. Lenses
a. Bi-convex
b. Plano-convex
c. Concavo-convex
Convex
Concave
d. Bi-concave
e. Plano-concave
f. Convexo-concave
P.A. Nagpure

4. Convex Lenses
principal axis
•
F
Thicker in the center than edges.
– Lens that converges (brings together) light rays.
– focus light rays to a focal (F) point in front of the lens.
– Forms real images and virtual images depending on position
of the object
P.A. Nagpure

5. Concave Lenses
Lenses that are thicker at the edges and thinner at the center
- Lens that make light rays diverge (spread out).
- If the rays of light are traced back (dotted sight lines), they all
intersect at the focal point (F) behind the lens.
principal axis
•
F
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6. Terminology
 The line joining the centres (C1 & C2) of the curvatures of
spherical surfaces is called principal axis.
•
O
Optic
centre
•
C1
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principal axis
•
C2
 If a ray of light is incident on a lens in such a direction that after
refraction, the emergent ray is parallel to the incident ray, then
the point of intersection of the refracted ray with the principal
axis is called the optical centre (O).

7. Terminology
 If the light rays incident parallel to the principal axis, after refraction
through the lens intersect the principal axis at the point called as focal
point or focus and
 its distance (f) from the optical centre of the lens is called focal length
of the lens. The plane perpendicular to principal axis and passing
through the focus is called focal plane.
 The plane perpendicular to principal axis and passing through optical
centre is called principal plane.
•
O
Optical
centre
f
Focal length
P.A. Nagpure

8. Terminology
 The power of lens is the measure of its ability to converge (bend
towards principal axis) the parallel rays of light.
 The power of convex lens is taken as positive while the power of
concave lens is taken as negative.
 The convex lens of large focal length produces small convergence
while the convex lens of small focal length produces large
convergence.
 Thus power lens is inverse of its focal length.
 The unit of power of lens is called a diopter (D).
 1 diopter = 1 (meter)-1
 For example: The convex lens of
focal length 2 meter has power 0.5 diopter
and the concave lens of focal length
2 meter has power - 0.5 diopter.
•
O
f
Focal length
P.A. Nagpure

9. Thin lens
• If the thickness of lens is negligible as compared to the radii of
curvature of its surfaces, the lens is said to be thin.
• Here we can neglect its thickness and hence it becomes easier to
predict the position and size of the image using simple lens
equation.
Where: u and v are the distances of the object and image from lens.
P.A. Nagpure

10. Following conventions of the signs are used to obtain the
relations between the quantities related to lenses.
 The diagrams are drawn showing the incident light travelling
from left to right.
 The distances are measured by taking the optical centre O of
lens as the origin.
 All the quantities measured right to the optical centre are
taken as positive while those measured left to the optical
centre are taken as negative.
 OP is positive
 OA is negative
Sign Conventions
X
O
Y
Direction of light
B
A
P
Q
P.A. Nagpure

11.  The heights measured upward and perpendicular to
principal axis are taken as positive and those downward are
taken as negative.
 AB is positive
 PQ is negative
 The angle made by a ray with the principal axis is taken as
positive, if on rotating in anticlockwise direction, it will be
along principal axis. Otherwise it is negative.
Sign Conventions
O
Y
Direction of light
B
A
P
Q
P.A. Nagpure

12. Deviation by a thin lens
Let a incident ray on thin lens parallel to
principal axis at height h. After refraction
it will pass through focus F, as shown in
figure .
The deviation produced by lens is given by
d
F
h
f
d
In the paraxial region δ being small,
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13. Deviation by a thin lens
d
I
Now consider point object at point O and its
corresponding image at I. (figure) θ1 θ2
O
A
-u v
h
A/c to lens equation
As
This shows that the deviation produced by a lens is independent of
the position of the object.
P.A. Nagpure

14. Equivalent Focal Length of Two Thin Lenses
d
d1
d
d2
F F’
L1 L2
Consider simple coaxial
optical system consists of two
thin lenses L1 & L2 placed on
common axis separated by
distance d, as shown in figure
Deviation d1 produced by lens L1 .
C A’
h1
f1
f2
h2
B’
A B
Deviation d2 produced by lens L2.
Total deviation d produced by the combination of lenses L1 & L2.
d = d1 + d2
………(1)
………(2)
………(3)
P.A. Nagpure

15. Equivalent Focal Length of Two Thin Lenses
From equation (1), (2), (3) & (4)
we have,
If f is equivalent focal length
of lens system, then
………(4)
………(5)
As Δ AA’F’ and Δ BB’F’ are similar,
therefore
d
d1
d
d2
F F’
L1 L2
C A’
h1
f1
f2
h2
B’
A B
Here AA’ = h1, AF’= f1, BB’= h2 and BF’= f1 - d
P.A. Nagpure

16. Equivalent Focal Length of Two Thin Lenses
d
d1
d
d2
F F’
L1 L2
C A’
h1
f1
f2
h2
B’
A B
Here AA’ = h1, AF’= f1, BB’= h2
and BF’= f1 - d
………(6)
From equation (5) & (6)
P.A. Nagpure

17. Equivalent Focal Length of Two Thin Lenses
Power of combination of two
thin coaxial lenses
equivalent focal length f is positive
i.e. the equivalent lens system is convergent.
equivalent focal length f is negative
i.e. the equivalent lens system is divergent.
P.A. Nagpure