Problems in lenses and mirrors - Problem L2
We have seen rearview mirror used in vehicles.
This mirror is used to keep an eye on all the traffic behind you.
Convex mirror is used as a rear view mirror because they give an erect and virtual image of the distant objects.
And the image formed by a convex mirror virtual, erect and diminished.
And therefore it can form an image of a large area in a small mirror.
Now, we will study the problems related to mirrors and lenses.
Let’s understand the problems in lenses and mirrors.
Suppose, a biconvex lens of focal length
1
5
c
m
is placed in front of a plane mirror.
The distance between the lens and the mirror is
1
0
c
m
.
Now, small object is kept at a distance of
3
0
c
m
from the lens.
Let’s see the formation of the image with lens and mirror.
The focal length of the biconvex lens is
1
5
c
m
.
A small object is placed at a distance of
3
0
c
m
from the lens that is at a distance of
2
f
.
Therefore, the image should form at
3
0
c
m
from the lens at
I
1
​
.
But since the ray strikes the plane before reaching
I
1
​
, the image
I
1
​
acts as the virtual object for reflection on the plane mirror.
And that is kept at a distance of
2
0
c
m
from it.
It will produce image
I
2
​
but as the ray encounters the lens, it gets refracted.
And the final image is formed at
I
3
​
.
For the last refraction from the biconvex lens, the object distance is shown as,
Now, we use lens formula to find the image distance.
A lens formula relates the object distance
u
, and image distance
v
to the focal length
f
of the lens.
Substitute all the values in the lens formula as
Now, solve this equation and find the image distance.
Therefore, a real image is formed at a distance of
1
6
c
m
from the plane mirror.
Revision
A lens formula relates the object distance
u
, and image distance
v
to the focal length
f
of the lens.
The End