16. An object is placed 15 cm in front of a convex lens. If focal length of the lens is 20 cm, find the
position and magnification of the image formed.
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Answer:
Given: For convex lens u=−15cm f=10cm
To find: v
Solution: From lens formula
1v−
u
1
=
f
1
v
1
+
15
1
=
10
1
v
1
=
30
1
v=30cm
And magnification is =
−15
30
=−2
So for image is inverted and magnified and when a mirror is placed at a distance d behind lens then u for mirror is u
1
=−30+α
=α−30
and v=−30−14+α
From mirror formula
v
1
+
u
1
=
f
1
α−45
1
+
α−30
1
=
10
−1
(α−45)(α−30)
α−30+α−45
=
10
−1
(α−45)(α−30)
2α−75
=
10
−1
20α−750=−α
2
+75α−1350
α
2
=
−
+
(55)
2
−4/100
2
α=
2
55+−25
=40cm or 15cm
Hence d=15cm(as 40 cm not possible)
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