Two identical thin plano-convex glass lenses (refractive index 1.5) each having radius of curvature of 20 cm are placed with their convex surfaces in contact at the centre. The intervening space is filled with oil of refractive index 1.7. The focal length of the combination is

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(3) -50 cm. Given: two identical thin plano-convex glass lenses (μ=1.5, R=20 cm) touching at their convex faces, with oil of μ=1.7 filling the lens-shaped gap. Idea: the oil fills the space between two convex surfaces, so it forms a bi-concave oil lens; the stack is three thin lenses in contact. Each glass lens: 1/(f_g)=(1.5-1)(1/(20)-1/∞)=0.025 cm⁻¹. Oil lens, radii -20 cm and +20 cm: 1/(fₒ)=(1.7-1)(-1/(20)-1/(20))=-0.07 cm⁻¹. 1/F=0.025-0.07+0.025=-0.02 cm⁻¹ F=-50 cm

Two identical thin plano-convex glass lenses (refractive index 1.5) each having radius of curvature of 20 cm are placed with their convex surfaces in contact at the centre. The intervening space is filled with oil of refractive index 1.7. The focal length of the combination is

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