a concave lens has focal length of a 20 cm.At what distance from the lens a 5cm tall object is placed so that it form a image at 15 cm from lens? Also calculate the image formed.
Answers
h = 5 cm
v = 15 cm
we know
1/F = 1/V - 1/U
1/20 = 1/15 -1/U
1/U =1/15 - 1/20
I think so this is the way for doing this
rest you can complete
after getting u
m = h'/h =v/u
h'= v/u * h
whre h' is the hight of image
ExplanatioAccording to the question,
Image distance, v=−15 cm (negative due to convex lens)
Focal length, f=−20 cm
Let the object distance be u.
By lens formula:
v
1
−
u
1
=
f
1
[4pt]
⇒
−15 cm
1
−
u
1
=
−20 cm
1
[4pt]
⇒
u
1
=
20 cm
1
+
−15 cm
1
[4pt]
⇒
u
1
=
60 cm
3−4
=
60 cm
−1
[4pt]
⇒u=−60 cm
Therefore, object is placed at 60 cm away from the lens, on the same side as image.
Now,
Height of object, h
1
=5cm
Magnification, m=
h
1
h
2
=
u
v
Putting value of v and u:
Magnification, m=
5 cm
h
2
=
−60 cm
−15 cm
⇒
5 cm
h
2
=
4
1
⇒h
2
=
4
5 cm
=1.25 cm
Thus, the height of the image is 1.25 cm and the positive sign means the image is virtual and erect.n: