(a)
We have to show that a thin converging lens of
focal length f followed by a thin diverging lens of focal length –f
will bring parallel light to a focus beyond the second lens provided
the separation of the lenses L satisfies
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Solution: Click For PDF Version The separation between the two lenses is L. As the parallel light strikes first the converging lens of focal length f, a real image will be formed at the right of the converging lens at a distance f from the lens. If ,
the image formed by the first lens will be to the right of the
diverging lens, whose focal length is –f.
The object distance with respect to the second lens will be
as it sees that the converging rays from the first lens which strike
it are coming from a virtual source to the right
of it. The image distance
can therefore be determined from the thin lens formula. We have
We have
assumed that
(b)
We consider
next the image formation when the converging and the diverging
lenses have been interchanged. The diverging lens of focal length –f
will focus incident parallel light as a virtual image at a distance
f to the left of it.
The second lens which is a converging lens of focal length f
is placed at a distance L
to the right of the diverging lens. With
respect to the converging lens in the sign convention that we are
using the object distance will be
which is positive. Therefore, the final image will be real and its location will be at the right of the second lens. (c)
When
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(b) We have to find whether this property
changes if the lenses are interchanged. (c)
We have to answer what happens when
.
.
Therefore, as
,
as the object is on the V-side
and diverging beam strike it. Therefore, the image will
be formed at distance
,
which can be determined using the thin lens formula. We have