6.4 THIN LENS FORMULA

6.4 THIN LENS FORMULA

6.4.1 Experiment to:

(i) investigate the relationship between object distance, u and image

distance, v for a convex lens.

(ii) determine the focal length of a thin lens using lens formula :
1 11
=+

6.4.2 Solve problems using lens formula for convex and concave lens.

Relationship between object distance, u, image
distance, v and focal length, f

a) Position of the camera lens near from the b) Position of the camera lens far from the
object produced bigger image object produced smaller image

Diagrams show images formed by different object distance from camera lens but
same focal length.

Relationship between object distance, u, image
distance, v and focal length, f

Conduct experiment 6.3
From the experiment :

i. The value of + is constant.This value same with .

ii. Graph of against is a straight line with gradient equal to -1. From = + , we can
deduce
a. Interception of horizontal axis = .

b. Interception of vertical axis = .
iii. When object distance increase, the image distance decrease.

A. Thin lens formula shows the relationship between object distance, u, image
distance, v and focal length, f for a lens as :
1 11
=+

B. Sign that must be obeyed in lens formula for convex and concave lens :

Focal length, f Positive (+) Negative ( - )
Image distance, v
Convex lens (converging lens) Concave lens (diverging lens)

• Real image • Virtual image
• Image formed at the site that • Image formed at the site that is

opposite with the object same as the object

SOLVE PROBLEMS USING LENS
FORMULA

Example 1
A piece of thin convex lens of focal length 12 cm. Determine the characteristics,
position and linear magnification of image when the object distance is :
a) 18 cm
b) 4 cm

SOLUTION b. u = +4 cm, f = +12 cm
1/v = 1/f – 1/u
a. u = +18 cm, f = +12 cm = 1/12 – 1/4
1/v = 1/f – 1/u v = -6 cm
= 1/12 – 1/18 Linear magnification, m = v/u
v = +36 cm = 6/4
Linear magnification, m = v/u = 1.5
= 36/18 Characteristics of image : virtual, upright,
=2 magnified.
Characteristics of image : real, inverted, Position of image : 6 cm from the lens
magnified. and is same side with the object.
Position of image : 36 cm from the lens Image formed 1.5 times larger than the
and is opposite with the object. object.
Image formed 2 times larger than the
object.

Example 2:
An object of height 9 cm is placed at a distance of 60 cm from a concave lens of focal length 30
cm. Determine the position and the size of image formed. State the characteristics of image.

u = +60 cm, f = -30 cm
1/v = 1/f – 1/u

= 1/-30 – 1/60
v = -20 cm
Linear magnification, m = hi/ho = v/u

hi/ 9 = 20 /60
hi = 3 cm

Characteristics of image : virtual, upright, diminished.
Position of image : 20 cm from the lens and is same site with the object.
Height of image is 3 cm.

Example 3 :
Diagram shows a straight wire put at the principle axis of a piece of
thin convex lens with focal length of 12 cm. X and Y are 24 cm and
18 cm from the lens.A cricket takes 6 second to move from X to Y.
Calculate the speed of the image cricket.

Solution :

EXCERCISE