A thin concavo-convex glass lens (refractive index 1.5 ) features a convex surface with a 20 cm radius of curvature and a concave surface with a 60 cm radius of curvature. The convex side is silvered and rests on a horizontal surface. A pin is initially positioned on the axis such that its image coincides with it. If the concave section is subsequently filled with water ( = 4/3 ), determine the distance through which

Step-by-step solution

For the glass lens, the top surface is concave and the bottom surface is convex. Since it rests on the convex surface, light from the pin enters the concave surface. Taking the downward direction as positive, the radius of the first surface is R₁ = -60 cm and the radius of the second surface is R₂ = -20 cm. The power of the glass lens is given by: P_g = ( _g - 1) ( 1 R₁ - 1 R₂ ) P_g = (1.5 - 1) ( 1 -60 - 1 -20 ) = 0.5 ( 1 20 - 1 60 ) = 1 60 cm ⁻¹ The bottom surface is silvered and acts as a mirror for light traveli