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

А сonvex lens is in contact with concave lens. The magnitude of the ratio of their powers is `2/3`. Their equivalent focal length is 30 cm. What are their individual focal lengths (in cm)?

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?

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).

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 of focal length f₁ is kept in contact with a concave lens of focal length f₂. Find 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?

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.