Effective Focal Length
Reflection and Refraction of light produces some beautiful scenery around us
The formation of Rainbow is due to the Refraction of Light
The reflection of the setting sun on the water produces a stunning visual treat
Humans have also artificially created some of the life-altering things based on these phenomena
The simple plane-mirror in which we see our reflection almost everyday, is based on the Reflection of Light
Spectacles, helping people with a defect in their eyes to see, uses Refraction of Light
Let us see the Image Formation Process in a Lens
If we consider a convex lens, we know the ray of light coming from infinity will merge at the focus after refraction
We know that the rays of light passing through the optical centre of the lens remains undeviated
And the ray of light passing through the focus will become parallel to the principle axis after refraction
Combining these two rays, the image formed will be real and inverted in nature
The image distance will be given by the lens law
$v1 −u1 =f1 $
$v1 −u1 =f1 $
Where
v= Image Distance
u= Object Distance
f= Focal Legth of the Lens
Let us now move forward and see the Image Formation by combining two lens
Let us join two lenses
$L_{1}$
and
$L_{2}$
with focal lengths,
$f_{1}$
and
$f_{2}$
Had
$L_{2}$
been not there, let the image by
$L_{1}$
be at
$I_{1}$
, such that the image distance is
$v_{′}$
Using the lens formula for
$L_{1}$
,
$f_{1}1 =v_{′}1 −u1 $
For the lens
$L_{2}$
, the virtual object will be at
$I_{1}$
and the image formed will be at
$I$
So, by using the same lens formula for lens
$L_{2}$
,
$f_{2}1 =v1 −v_{′}1 $
we will get the focal length of the lens
$L_{2}$
Now we replace the combination by a single lens and we need the focal length of the lens that will place the image at the same point
$I$
By using the lens formula for lens
$L$
we get the focal length for L,
$f1 =v1 −u1 $
Adding equation (1) and (2),
$f_{1}1 +f_{2}1 =v_{′}1 −u1 +v1 −v_{′}1 $
Thus,
$f_{1}1 +f_{2}1 =v1 −u1 $
Therefore, for the combination of two lenses the effective focal length is given by,
$f_{1}1 +f_{2}1 =f1 $
For combination of n lenses,
$f_{1}1 +f_{2}1 +......=f1 $
Revision
Effective focal length for combination of two lenses is,
$f_{1}1 +f_{2}1 =f1 $
Effective focal length for n lenses will be given by,
$f_{1}1 +f_{2}1 +......=f1 $
The End