A point object O is placed along X-axis. An equi-convex thin lens (µ g = 1.5 ) of focal length f = 20 cm in air is placed so that its principal axis is along X-axis. Now the lens is cut at the middle (along the principal axis) and upper half is shifted along X-axis and Y-axis by 20 cm and 2 mm respectively and right side of lower half is filled with water (µ w = 4/3). Locate the positions of all images formed by thin system.
Text Solution
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Sol.
Case I : Image formed by L 1
F = + 20 cm
m = 
= 
u = – 80 cm
= 
× 
v = 
= 
cm
⇒ I = – 
mm
∴ X-co-ordinate = 80 + 
= 
cm
∴ Y-co-ordinate = 
mm = 
mm
Hence, co-ordinate of image formed by
L 1 = 
Case II : Image formed by L 2
For equiconvex lens 
= (µ – 1) 
= 
Now, consider refraction at air-water or, interface
or v = 30 cm
R = f = 20 cm
– 
= 
– 
= 
or v' = 80 cm
∴ X-co-ordinate = (80 + 60) = 140 cm
As the object lies on principal axis, image will be formed on the X-axis itself
Hence, co-ordinate of image formed by L 2
L 2 = (140 cm, 0)
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