Two thin convex lenses L 1 and L 2 having focal length f 1 = 30 cm. and f 2 = 60 cm. respectively are placed co-axially as shown in Fig. A plane mirror is placed normal to the axis and a point luminous object O on the axis as shown in the figure. Light rays emitted by O first pass though lenses L 1 and L 2 respectively and then reflect from mirror M and then reflected rays pass through the lenses L 2 and L 1 respectively. Calculate position of final image of O.
Text Solution
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Sol. Assuming direction of propagation of incident paraxial rays to be positive x-direction.
Considering refraction through lens L 1 , u = – 45 cm, f = + 30 cm, v = v 1 (suppose)
Using lens formula 
– 
= 
, v 1 = 90 cm
It means that just after refraction through lens L 1 , image is formed at a distance 90 cm from L 1 and on right of it. But that is pole of L 2 .
Therefore, for L 2 , object is at its pole. Hence, image formed by it coincides with the object.
This image behaves like an object for plane mirror. It means for plane mirror, object is 90 cm in front of it. Hence, after reflection through it, image is formed 90 cm behind it or 180 cm on right of lens L 2 .
Now reflected rays travel leftwards. Hence, for further refractions leftward direction is to be considered positive.
For refraction through lens L 2 ,
u = – 180 cm, f = + 60 cm, v = v 2 (let)
Using lens formula, v 2 = + 90 cm
It means just after refraction of reflected rays through lens L 2 , image is formed at pole of L 1 .
Whenever an object is at pole of a lens, image coincides with the object. Hence, the final image is at pole of lens L 1 .
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