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Question
Consider three converging lenses L1, L2 and L3 having identical geometrical construction. The index of refraction of L1 and L2 are \[\mu_1 \text{ and } \mu_2\] respectively. The upper half of the lens L3 has a refractive index \[\mu_1\] and the lower half has \[\mu_2\] following figure . A point object O is imaged at O1 by the lens L1 and at O2 by the lens L2placed in same position. If L3 is placed at the same place,
(a) there will be an image at O1
(b) there will be an image at O2.
(c) the only image will form somewhere between O1 and O2
(d) the only image will form away from O2.
Solution
(a) there will be an image at O1
(b) there will be an image at O2
The lens L1 converges the light at point O1 and lens L2 converges the light at O2. As the upper half of lens L3 has a refractive index equal to that of L1, it will converge the light at O1 and thus the image will be formed at O1. Also, the lower half of lens L3 has a refractive index equal to that of lens L2, it will converge the light at O2 and thus the image will be formed at O2.
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