Question

Two plano-convex lenses (1 and 2) of glass of refractive index 1.5 have radii of curvature 25cm and 20cm. They are placed in contact with their curved surfaces towards each other and the space between them is filled with liquid of refractive index 4/3. The combination is: 

• A. convex lens of focal length 70cm
• B. concave lens of focal length 70cm
• C. concave lens of focal length 66.6cm
• D. convex lens of focal length 66.6cm

Hint:

When lenses are immersed in a liquid: P = (fracnlensnmₑdᵢᵤm - 1)((1)/(R₁) - (1)/(R₂)) Lower refractive contrast increases focal length.

Answer 1

The Correct Option is A

Step 1: Refractive indices ng = 1.5, nm = (4)/(3) Effective refractive factor: ((ng)/(nm) - 1) = ((1.5)/(4/3) - 1) = 0.125

Step 2: Power of the combination P = 0.125((1)/(25) + (1)/(20)) P = 0.125 × 0.09 = 0.01125 

Step 3: Focal length f = (1)/(P) ≈ 70 cm Since power is positive, the combination behaves as a convex lens.