When the gap between two identical concave thin lenses μ = 3 2 , f = 10 cm placed in contact is filled with certain liquid, the image of an object placed at 15 cm from lens combination shifts away from the lens by 5 4 cm . If the refractive index of the liquid is μ , then write 3 μ as your answer.

Step-by-step solution

In case (i) (without liquid) 1 v - 1 - 15 = 2 f ⇒ 1 v = - 1 5 - 1 15 = - 4 15 ⇒ v = - 3.75   cm When the gap is filled with liquid v ' = - 3.75 - 1.25 = - 5   cm ⇒ - 1 5 - 1 - 15 = - 1 5 + ( μ l - 1 ) ( 2 R ) Here, 1 10 = 3 2 - 1 2 R   ⇒ R = 10   cm Hence, - 2 15 = - 1 5 + μ l - 1 5 ⇒ μ l = 4 3