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.

Answer 1

(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.