A converging lens with a focal length of +20 cm is located 10 cm to the left of a diverging lens having a focal length of -15 cm. A real object is located 40 cm to the left of the first lens. We have to locate and describe the image formed.
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Solution: Click For PDF Version We will solve this problem in two steps. In the first step we will find the image formed by the first lens of a real object which is 40 cm to the left of the lens of focal length .
Let
be the distance of the image from the first lens. Using the thin
lens formula, we have
This image is real and inverted and is formed at location 40 cm to the right of the first lens. But, this image will not be seen as such as there is intervention of the second lens of focal length -15 cm, which is located 10 cm to the right of the first lens. As
the image formed by the first lens is in the ‘transmitted-side’
of the second lens, it will be virtual with respect to it and
therefore the object distance of the image formed by the first lens
with respect to the second lens will be
The final image formed by the two lenses will be virtual and at a distance of 20 cm to the left of the first lens. We next work out the lateral magnification.
We thus find that the final image will be virtual and of the same size as the object and will be formed at a distance of 20 cm to the left of the first lens. |
,
and as
,
the image distance
will be given by
