a lens form real image of an object 20 CM away from lens. A second Len is kept in contact with this lens, then image shifts 10cm towards the lens combination ? Find power of another lens.
Answers
Answer:
5
Explanation:
As image formed is real, therefore lens must be convex, v=20cm.
Let f
1
, be the focal length for this lens and f
2
be the focal length of the other lens put in contact later.
for the first lens,
∴
f
1
1
=
v
1
1
−
u
1
1
=
20
1
−
u
1
1
-----------------(1)
After placing it in contact with another lens, the image shifted to 10cm towards the combination
i.e., v
2
=(20−10) cm=10 cm
Let f
net
be the effective focal length of the combination, which can be given as:
∴
f
net
1
=
f
1
1
+
f
2
1
=
v
2
1
−
u
2
1
=
10
1
−
u
1
1
⇒
f
1
1
+
f
2
1
=
v
2
1
−
u
2
1
=
10
1
−
u
1
1
--------------(2)
From equation (1) and (2):
10
1
−
u
1
=
f
1
1
+
f
2
1
=[
20
1
−
u
1
]+
f
2
1
⇒
10
1
−
u
1
=
20
1
−
u
1
+
f
2
1
⇒
10
1
=
20
1
+
f
2
1
⇒
10
1
−
20
1
=
f
2
1
⇒
f
2
1
=
20
1
Hence, f
2
=20cm
∴P=
20
100
m
−1
=5D