A concave lens of focal length 20cm forms an image 20 cm from the lens. How far is the object placed from the lens. If concave lens is replaced by convex lens. What will be the height of image and nature of the image if height of the object is 15cm.
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the Answer:
According 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, the object is placed at 60 cm away from the lens, on the same side as the image.
Now,
Height of object, h
1
=5cm
Magnification, m=
h
1
h
2
=
u
v
Putting the 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.
Explanation:
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