Linear Magnification (m)  
Magnification is a measure of the extent to which an optical system enlarges or  
reduces an image in relation to the object.  
( )  
풉풆풊품풉풕 풐풇 풊풎풂품풆 풉풊  
풊풎풂품풆 풅풊풔풕풂풏풄풆(풗)  
풐풃풋풆풄풕 풅풊풔풕풂풏풄풆(풗)  
풎 =  
=
(
)
풉풆풊품풉풕 풐풇 풐풃풋풆풄풕 풉풐  
The Lens Formula  
• Consider the figure below, an object h is placed in a convex mirror of focal  
length f, whereby u is the object distance and v is the image distance  
• From the figure above, the following triangles are equiangular, ie,. ∆ 푨푶푩 ~∆  
푨′푶푩′, 풂풏풅 ∆푶푪푫 ~∆푨′푩′푫  
• Now consider,  
,
• Also consider,  
,
Then compare equation (i) and (ii)  
풖풗 − 풖풇 = 풇풗  
→ 풖풗 = 풗풇 + 풖풇 = (풖 + 풗)풇  
풖풗  
풇
ퟏ
풇
풖
풗
ퟏ
풗
ퟏ
풖
(
)
풖풗 = 풖 + 풗 풇 →  
= 풖 + 풗 →  
=
ퟏ
+
=
+
풖풗  
풖풗  
ퟏ
풇
ퟏ
풖
∴
=
+
thelensformulais given b:y  
풗
Real-Is-Positive Convention  
To calculate the values of u and v, a sign rule or convention is adopted. The rule is  
referred to as the real-is-positive convention.  
❖ Sign for real object and image  
Sign for virtual object and image are  
are  
u = +  
v = -  
and  
and  
v = + ❖  
u = -  
❖ Sign of virtual object and image is negative. Because the principal focus of  
a concave lens is virtual  
NB;  
❖ For a convex lens, 풇 is positive and for a concave lens, 풇 is negative.  
❖ If image is above the principal axis, object height will be positive. It means  
that the image formed is upright and virtual  
❖ If image is below the principal axis, object height will be negative. It means  
that the image formed is inverted and real  
❖ m is positive (+) for an image that is upright with respect to the object.  
❖ m is negative (-) for an image that is inverted with respect to the object.  
Works examples  
1. An object 1.0 cm high is 8.0 cm to the left of a convex lens that has a 6.0 cm  
focal length.  
Find the image location and image height.  
Solution; given; 풉풐 = ퟏ풄풎, 풖 = ퟖ풄풎, 풇 = ퟔ풄풎, 풗 =? 풉풊 =?  
From;  
cm  
But;  
Thus;  
Therefore; the image formed is 24 cm to the right of the lens, and 3cm high  
(3 times the object’s size)  
Images formed by thin Lenses  
Characteristics of the Image Formed by a Convex Lens  
• As with a curved mirror, the position and size of an image can be found by  
drawing a ray diagram.  
• Any two of the following three rays are sufficient to fix the position and size of  
the image.  
• The characteristics, position and size of the image formed by a convex lens  
depends on the object distance (u) relative to the focal length (f)  
Images Formed by Convex Lens  
Image formed in Concave Lens  
• Concave lenses create only virtual images. After the rays are refracted, they  
never converge and so there will be no real images.  
• All concave lens images will be upright, virtual, and diminished, and can be found  
between the F and the lens for all object positions.  
Properties of image formed  
• Virtual  
• Formed between the object and the lens  
• Erect  
• Diminished  
• As U increase to infinity also V increase to F  
Worked example  
1. Describe how a convex lens could be used to make a magnifying lens.  
ANS; A convex lens increases the size of the image if the object is inside 2F.  
However, the image will be inverted if the object is between F and 2F.  
Therefore, a convex lens will make a good magnifying lens if the objects being  
observed are inside the focal point.