In the given figure there are two thin lenses of same focal length f arranged with their principal axes inclined at an angle α . The separation between the optical centres of the lenses is 2f . A point object lies on the principal axis of the convex lens at a large distance to the left of the convex lens.
Text Solution
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Sol. The image will be formed at the focus of the convex lens after refraction through the convex lens (at I).
Now for the concave lens, I acts as an object.
Since the distance is always taken from the pole on the principal axis.
If it can be assumed that the point I is the tip of an object erected on the principal axis of the concave lens, the image of point I will be the tip of the final image (let it be I′).
Distance of object = u = f cos α .
Applying lens formula, 
– 
= 
or 
– 
= 
= 
v = 
Now distance O′I′ = 
× 
So x-coordinate of I′ = OO′ – O′I′ = 2f – 
f 
= f 
y-coordinate = 0.
So coordinates of image are 
.
We can verify the result by putting α = 0.
Coordinates after putting α = 0
= 
.
This result is right if the principal axes of both the lenses coincide, then the image will be formed finally) at x = 
.
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