A converging lens of 5 cm focus distance is placed in contact with 10 converging lens of less focus distance, find the focal length of the composite system
Answers
Explanation:
The first image will be formed from refraction from lens, its position can be determined by lens formulas
The lens formulas is given as
v
1
−
u
1
=
f
1
...(i)
where u=−a,f=+f, substituting values in equation (i)
v
1
−
−a
1
=
f
1
⇒v=
a−f
af
The image formed will be left side of lens provide a>f
The mirror will form the image at right side of the lens with distance equal to
a−f
af
Now the third image will be formed by lens again for which the coordinate system will be reversed of earlier as the rays are traveling from left to right:
u=
a−f
af
, f=+f and v=
3
a
applying lens formulas
v
1
−
u
1
=
f
1
...(i)
a
3
−
af
a−f
=
f
1
...(ii) multiplying and dividing by f
af
3f
−
af
a−f
=
af
a
3f−a+f=a⇒a=2f
Explanation:
The first image will be formed from refraction from lens, its position can be determined by lens formulas
The lens formulas is given as
v
1
−
u
1
=
f
1
...(i)
where u=−a,f=+f, substituting values in equation (i)
v
1
−
−a
1
=
f
1
⇒v=
a−f
af
The image formed will be left side of lens provide a>f
The mirror will form the image at right side of the lens with distance equal to
a−f
af
Now the third image will be formed by lens again for which the coordinate system will be reversed of earlier as the rays are traveling from left to right:
u=
a−f
af
, f=+f and v=
3
a
applying lens formulas
v
1
−
u
1
=
f
1
...(i)
a
3
−
af
a−f
=
f
1
...(ii) multiplying and dividing by f
af
3f
−
af
a−f
=
af
a