Two thin convex lenses 
and 
having focal length 
and 
respectively are placed coaxially as shown in figure. A plane mirror is placed normal to the axis and a point luminous object 
on the axis as shown in figure. Light rays emitted by 
first pass through lenses 
and 
respectively and then reflect from mirror 
and then reflected rays pass through the lenses 
and 
respectively, Calculate position of final image of 
.
and 
Text Solution
Verified by ExpertsA
Suppose direction of propagation of the incident paraxial rays is in the positive 
-direction.
Considering lens 
,
∴ Image is formed at a distance 90 cm from 
and is on right of it, just after refraction through lens 
. But that is the pole of 
.
For 
, object is at its pole.
∴ Image formed by 
coincides with the object for 
.
This image behaves like an object for plane mirror,
∴ For plane mirror, object is at 90 cm in front of it.
∴ After reflection through it, image is formed 90 cm behind it or 180 cm on right of lens 
.
Now the reflected ray travels leftward. For refraction through lens 
, 
(considering leftward directions to be positive)
Applying lens formula, 
∴ Just after refraction of reflected rays through lens 
, image is formed at pole of 
.
Whenever object is at pole of a lens, image coincides with the object. Hence, the final image is at pole of lens 
.
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