Number of images formed by two concave lens, one displaced from optical axis

In summary, when a point object is placed in the left of a biconvex symmetrical lens cut in two halves, the lens-makers formula shows that the focal length of the upper and lower parts are the same. However, due to the slight difference in position of each part, the image formed by each will be at a slightly different distance from the object. Therefore, the correct answer is (b) Three images will be formed, contrary to the answer given in the book.
  • #1
Sumedh
62
0

Homework Statement


A biconvex symmetrical lens is cut in two halves and placed as shown in figure.
if a point object is placed in the left how many images will be formed
options - (a) Two images
(b) Three images


Homework Equations





The Attempt at a Solution



As I have used the lens makers formula the focal length of upper part and lower part is same
so they will form images that coincides and hence one image will be formed and the other image will be formed by the middle (thick overlapping part)
so finally 2 images will be formed.
but the answer that is given in my book is (b)Three images will be formed.

I will be very thankful even if hints are provided.
 

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  • #2
Sumedh said:

Homework Statement


A biconvex symmetrical lens is cut in two halves and placed as shown in figure.
if a point object is placed in the left how many images will be formed
options - (a) Two images
(b) Three images

Homework Equations


The Attempt at a Solution



As I have used the lens makers formula the focal length of upper part and lower part is same
so they will form images that coincides and hence one image will be formed and the other image will be formed by the middle (thick overlapping part)
so finally 2 images will be formed.
but the answer that is given in my book is (b)Three images will be formed.

I will be very thankful even if hints are provided.

While the lens-makers formula shows the upper part and lower part have the same focal length, the position of each is slightly different.
Unless the object is placed at "infinity", the image formed by each part will be at slightly different distances from the object.

EDIT: Note you have drawn a bi-concave lens, not a bi-convex lens! Perhaps you just used the wrong name?
 
  • #3
PeterO said:
Perhaps you just used the wrong name?
I was sorry for that.

Thank you very much.
 

Related to Number of images formed by two concave lens, one displaced from optical axis

1. How many images can be formed by two concave lenses placed next to each other?

The number of images formed by two concave lenses placed next to each other depends on the position of the lenses with respect to the optical axis. If the lenses are aligned with the optical axis, only one image will be formed. However, if one of the lenses is displaced from the optical axis, two images will be formed.

2. Does the distance between the lenses affect the number of images formed?

Yes, the distance between the lenses can affect the number of images formed. If the distance between the lenses is increased, the number of images formed will also increase. This is because the light rays passing through the first lens will diverge further before reaching the second lens, resulting in multiple images being formed.

3. Why does a displaced concave lens create multiple images?

A displaced concave lens creates multiple images because the light rays passing through the lens are bent more than usual, due to the displacement. This causes the light rays to diverge further, resulting in multiple images being formed.

4. Can the number of images formed be controlled by changing the radius of curvature of the lenses?

Yes, the number of images formed can be controlled by changing the radius of curvature of the lenses. If the radius of curvature is increased, the lenses will become less concave, causing the light rays to bend less and resulting in fewer images being formed.

5. Is the number of images formed the same for all types of concave lenses?

No, the number of images formed can vary depending on the type of concave lens used. Lenses with a larger aperture or a higher refractive index will produce more images compared to lenses with a smaller aperture or lower refractive index.

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