e.g A concave lense f= 20cm & convex lens f= 30cm are
15 cm apart. Where should an object be placed, so
that its image is
at infinity
f=30cm
f = 15cm
25cm
Answers
Answer:
A concave lens of focal length 20 cm and a double convex lens of focal length 30 cm are placed 15 cm apart. The object is placed at a distance of x cm from the concave lens (presumably in the direction opposite to that of the convex lens) and the image formed by the combined system of lenses is at infinity.
The lens formula is 1v−1u=1f where, u,v and f are the distance of the object from the lens, the distance of the image from the lens, and, the focal length of the lens respectively.
As per the sign convention, for a concave lens, u,v and f are all negative. and for a convex lens, u, is negative and v and f are positive for a real image.
Let us first consider only the concave lens.
1v−1u=1f⇒1v=1f+1u.
⇒1v=u+fuf=−x−2020x.
⇒v=−20xx−20.
This image is the object for the convex lens.
⇒ The distance of the object from the convex lens is the distance of the image from the concave lens plus the distance of between the concave lens and the convex lens.
⇒ For the convex lens, u=−20xx−20−15.
Since the image formed by the combined system is at infinity, for the convex lens sub-system, the distance of the object from the lens is equal to the focal length of the convex lens.
⇒−20xx−20−15=−30⇒20xx−20=15.
⇒20x=15x−300⇒x=−60 cm.
Answer:
A concave lens of focal length 20 cm and a double convex lens of focal length 30 cm are placed 15 cm apart. The object is placed at a distance of x cm from the concave lens (presumably in the direction opposite to that of the convex lens) and the image formed by the combined system of lenses is at infinity.
The lens formula is 1v−1u=1f where, u,v and f are the distance of the object from the lens, the distance of the image from the lens, and, the focal length of the lens respectively.
As per the sign convention, for a concave lens, u,v and f are all negative. and for a convex lens, u, is negative and v and f are positive for a real image.
Let us first consider only the concave lens.
1v−1u=1f⇒1v=1f+1u.
⇒1v=u+fuf=−x−2020x.
⇒v=−20xx−20.
This image is the object for the convex lens.
⇒ The distance of the object from the convex lens is the distance of the image from the concave lens plus the distance of between the concave lens and the convex lens.
⇒ For the convex lens, u=−20xx−20−15.
Since the image formed by the combined system is at infinity, for the convex lens sub-system, the distance of the object from the lens is equal to the focal length of the convex lens.
⇒−20xx−20−15=−30⇒20xx−20=15.
⇒20x=15x−300⇒x=−60 cm.
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