Focal length of concave lens using convex lens

In summary, the conversation discusses the use of a convex lens with a focal length of 10 cm to form a real image of an object placed at a distance of 20 cm. A thin concave lens is then introduced midway between the convex lens and the position of the image, resulting in the image being formed 5 cm away from its previous position. The focal length of the concave lens is then questioned, with one method yielding a value of -30 cm, and the book stating a value of -5 cm. An error is suspected in the calculation of the concave lens's focal length, with the image expected to be farther away due to the lens's diverging nature.
  • #1
Amith2006
427
2
# 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.
 
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  • #2
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)?
 
  • #3
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?
 
  • #4
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.
 

What is the focal length of a concave lens?

The focal length of a concave lens is the distance between the lens and the point where parallel rays of light converge after passing through the lens.

How is the focal length of a concave lens measured?

The focal length of a concave lens is measured by placing the lens between an object and a screen and finding the distance between the lens and the screen where a clear image is formed.

How does a convex lens affect the focal length of a concave lens?

A convex lens placed in front of a concave lens increases the effective focal length of the concave lens, meaning the image formed will be further away from the lens.

What is the relationship between the focal length of a concave lens and the curvature of its surface?

The focal length of a concave lens is directly proportional to the curvature of its surface. As the curvature increases, the focal length decreases.

Can the focal length of a concave lens be negative?

Yes, the focal length of a concave lens can be negative if the lens is diverging light, meaning the light rays are spreading out after passing through the lens. This is in contrast to a positive focal length, where the light converges after passing through the lens.

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