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Solution


Q.

A thin plano convex lens made of glass of refractive index 1.5 is immersed in a liquid of refractive index 1.2. When the plane side of the lens is silver coated for complete reflection, the lens immersed in the liquid behaves like a concave mirror of focal length 0.2 m. The radius of curvature of the curved surface of the lens is          [2025]
1 0.15 m  
2 0.10 m  
3 0.20 m  
4 0.25 m  

Ans.

(2)

The system act as a concave mirror of focal length 0.2 metre, it means parallel rays of light gets focused at a distance 0.2 metre in front of the polished lens.

Using, μ2v–μ1u=(μ2–μ1)R

Here, μ1=1.2, μ2=1.5 and u=∞

1.5v–1.2∞=(1.5–1.2)R ⇒ v=5R

The image formed by the curved surface acts as virtual object for plane mirror and it will from a real image in front of the plane mirror. Now rays again interact with curved surface and form final image.

Again using, μ2v–μ1u=(μ2–μ1)R

Here, μ1=1.5, μ2=1.2, u=5R and v=0.2

1.20.2–1.55R=(1.2–1.5)–R ⇒ R=110m=10 cm