A biconvex glass lens of refractive index 1.5 has both radii of curvature equal to 20 cm . It is placed on a horizontal plane mirror. A few drops of a liquid are placed between the lens and the mirror, forming a plano-concave liquid lens. A small object is placed on the principal axis of the system. It is observed that the image of the object coincides with the object itself when it is at a distance of 30 cm from the

Step-by-step solution

For the image to coincide with the object (auto-collimation), the rays from the object must strike the plane mirror normally. This implies that the rays must emerge parallel to the principal axis after passing through the combination of the glass lens and the liquid lens. Therefore, the object must be placed at the focal point of the equivalent lens combination. Thus, the equivalent focal length of the combination is F_ eq = 30 cm = 0.3 m . The equivalent power of the lens combination is: P_ eq = 1 F_ eq = 1 0.3 =