The two surfaces of a biconvex lens has same radii of curvatures. This lens is made of glass of refractive index 1.5 and has a focal length 10 ~cm in air. The lens is cut into two equal halves along a plane perpendicular to its principal axis to yield two plano-convex lenses. The two pieces are glued such that the convex surfaces touch each other. If this combination lens is immersed in water (refractive index =4 / 3

Step-by-step solution

If a lens of focal length f is divided into two equal parts as shown in figure (1) and each has a focal length f^ then 1 f = 1 f^ + 1 f^ i.e., f^ =2 f i.e., each part will have focal length 2 f . Now if these parts are put in contact as in figure (2), then resultant focal length of the combination will be ' 1 F = 1 2 f + 1 2 f i.e., F=f (initial value) For this combination, 1 F = ( _a _g-1 ) ( 1 R₁ - 1 R₂ ) (i) Now, if this combination is immersed in liquid, then 1 F^ = ( _l _g-1 ) ( 1 R₁ - 1 R₂ ) (ii) F^ f = ( _a