Two convex lenses L₁ and L₂ of focal lengths 20 cm and 10 cm respectively are placed coaxially. A point object is placed at a distance of 30 cm in front of L₁ . A plane mirror is placed behind L₂ . It is observed that the final image of the system coincides with the object itself, and this condition holds irrespective of the distance of the plane mirror from L₂ . The separation between the two lenses is :

Step-by-step solution

For the final image to coincide with the object irrespective of the plane mirror's position, the rays striking the mirror must be normal to its surface. This implies that the rays emerging from lens L₂ must be parallel to the principal axis. For lens L₁ , applying the thin lens formula: 1 v₁ - 1 u₁ = 1 f₁ 1 v₁ - 1 -30 = 1 20 1 v₁ = 1 20 - 1 30 = 1 60 v₁ = +60 cm The image formed by L₁ acts as the object for L₂ . For L₂ to produce parallel emergent rays, its object must be located at its first principal focus. Since