CHAPTER 6 GEOMETRICAL OPTICS

Object Ray diagram Image
characteristic
distance, u
 Real
u = 2f O F1 F2 2F2  Inverted
back  Same size
2F1 I  Formed at point

Front 2F2. (at the back of
the lens)

 RIS

 Real

f <u< 2f 2F1 O F1 I  Inverted
 Magnified
Front F2 2F2
back  Formed at a
51 distance greater

than 2f at the

back of the lens.

RIM 49

Object Ray diagram Image
characteristic
distance, u
 Real or virtual
u=f O  Formed at infinity.

2F1 F1 F2 2F2
back
Front

u<f  Virtual

52  Upright

 Magnified

 Formed in front
of the lens.

VUM

I 2F1 F1 O F2 2F2
back
Front

50

Images formed by a convex (diverging) lens
• Figure shows the graphical method of locating an image formed

by a convex lens.
• Object position → any position in front of the diverging lens.

O F2 I F1
back
Front

• The characteristics of the image formed are VUD 53
– virtual
– upright

– diminished (smaller than the object)
– formed in front of the lens.

Example

An object is placed 50 cm in front of a thin biconvex
lens of focal length 20 cm. Use a ray diagram to locate
the image & discuss the characteristics of the image.

Scale : 1 cm : 10 cm Image properties :
Real, Inverted,
OF Reduced in size

I
F

u = 50cm v 54

Thin Lens Equation r= 2f
r= radius of curvature
1+1= 1
uv f
u = object distance
v = image distance
f = focal length

Magnification of Images

M = hi = − v hi = image height
ho u ho = object height
v = image distance

u = object distance

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Linear Magnification

m = − image distance, v = height of image, hi
object distance, u height of object, ho

If m > 1.0, image is larger than object or magnified
If m < 1.0, image is smaller than object or diminished
If m = 1.0, image is same size as the object
If m = +ve, image is upright
If m = -ve, image is inverted

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Sign Convention for Thin Lenses

Quantities Positive (+) Negative (–)

Object distance, In front of lens At back of lens
u ( Real object ) (Virtual object)
In front of lens
Image distance, v At back of lens
(Real) (Virtual)

Converging / Diverging /
Focal length, f convex lens concave lens

To use the thin lens equation correctly, be careful to use
the appropriate signs for all the known quantities. The
final answer will also have a sign, which gives additional
information about the system.

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Biconvex Convex Plano – convex
meniscus

Biconcave Concave Plano – concave
meniscus
58

Example

You are given a thin diverging lens. You find that a
beam of parallel rays spreads out after passing
through the lens as though all the rays came from a
point 20.0 cm from the center of the lens. You want
to use this lens to form an erect virtual image that is
1/3 the height of the object.

(a) Where should the object be placed ?

(b) Draw a principal ray diagram.

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Solution
f = – 20 cm = – 0.2 m
Lateral magnification, M = 1

3

from : M = − v
u

1=−v
3u

v = − u (1)
3

from Thin Lens Equation : 1 + 1 = 1
uv f

60

1 + 1 = 1 (2)
u v − 0.2

Substitute (1) into (2):

1 + 1 = − 1
u [− u] 0.2

3

1−3=− 1
u u 0.2

2= 1
u 0.2

u = 0.4 m

61

Substitute u = 0.4 m into (1) we can get image distance
v = 0.4 = 0.133 m
3

(b) Ray diagram :

u = 0.4
m

O FI F

62

End of Chapter 6

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