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 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?

Two thin convex lenses L₁ and L₂ of focal lengths f₁ and f₂, respectively, are placed coaxially in contact. An object is placed at a point beyond the focus of lens L₁. Draw a ray diagram to show the image formation by the combination and hence derive the expression for the focal length of the combined system.

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?

A thin lens made of a material of refractive index μ₂ has a medium of refractive index μ₁on one side and a medium of refractive index μ₃ on the other side. The lens is biconvex and the two radii of curvature have equal magnitude R. A beam of light travelling parallel to the principal axis is incident on the lens. Where will the image be formed if the beam is incident from (a) the medium μ₁ and (b) from the medium μ₃?

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 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?