Focal length of concave lens using convex lens

  1. # A convex lens of focal length 10 cm forms a real image of an object placed at a distance of 20 cm from it. Midway between the convex lens and the position of the image a thin concave lens is introduced. The image formed now is at a distance of 5 cm away from the earlier position. What is the focal length of the concave lens?
    I solved it in the following way:
    Case-1
    Let u, v and f be the object distance, image distance and the focal length of the convex lens.
    Here u = 20 cm, f = + 10 cm
    1/v = 1/f – 1/u
    1/v= 1/10 – 1/20
    v = 20 cm
    Case- 2
    Let u, v and f be the object distance, image distance and the focal length of the concave lens.
    Here u = - 10(virtual object), v = + 15 cm
    1/f = -1/10 + 1/15
    f = - 30 cm
    But the answer given in my book is – 5 cm.
     
  2. jcsd
  3. Gokul43201

    Gokul43201 11,141
    Staff Emeritus
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    I don't get 5 cm either.

    But I think you made a mistake with setting v=15cm in the second part. Would you expect the image for a concave lens to be 5cm closer to the lens or 5cm farther from it (compared to the object)?
     
  4. I assumed it to be away because i felt that concave lens is diverging in nature and so the image would be produced 5 cm away from the lens. What do you say?
     
  5. Gokul43201

    Gokul43201 11,141
    Staff Emeritus
    Science Advisor
    Gold Member

    That sounds right (that the image would be farther away). There must be a mistake with the way I was doing it. I'm too sleepy to think straight now. I'll look at this again when I find some free time. Meanwhile someone else might have something useful to say.
     
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