The convex side of a thin concavo-convex lens of glass of refractive index 1.5 has a radius of curvature of 20cm. The concave surface has a radius of curvature of 60cm. What is the focal length of the lens? The convex side is silvered and placed on a horizontal surface. What is the effective focal length of the silvered lens? The concave part is filled with water with refractive index 1.33. What is the effective focal length of the combined glass and water lens? If the convex side is silvered what is the new effective focal length of the silvered compound lens?

Explanation

To solve the problem step by step, we will break it down into parts as follows:

### Step 1: Calculate the Focal Length of the Concavo-Convex Lens

The formula for the focal length \( F \) of a lens made of a material with refractive index \( n \) and having radii of curvature \( R_1 \) and \( R_2 \) is given by:

\[
\frac{1}{F} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)
...