Refraction at a Spherical Surface and Lenses - Thin Lenses and Their Combination

An air bubble is formed inside water. Does it act as a converging lens or a diverging lens?

A single lens is mounted in a tube. A parallel beam enters the tube and emerges out of the tube as a divergent beam. Can you say with certainty that there is a diverging lens in the tube?

A point object is placed on the principal axis of a convex lens (f = 15 cm) at a distance of 30 cm from it. A glass plate (μ = 1.50) of thickness 1 cm is placed on the other side of the lens perpendicular to the axis. Locate the image of the point object.

The radii of curvature of a lens are + 20 cm and + 30 cm. The material of the lens has a refracting index 1.6. Find the focal length of the lens (a) if it is placed in air, and (b) if it is placed in water (μ = 1.33).

A converging lens is kept coaxially in contact with a diverging lens – both the lenses being of equal focal length. What is the focal length of the combination?

When two thin lenses are kept in contact, prove that their combined or effective focal length F is given by:

`1/F = 1/f_1  + 1/f_2`

where the terms have their usual meaning.

A convex lens is placed in contact with a plane mirror. A point object at a distance of 20 cm on the axis of this combination has its image coinciding with itself. What is the focal length of the lens?

A convex lens of focal length f₁ is kept in contact with a concave lens of focal length f₂. Find the focal length of the combination.