Refraction at Spherical Surfaces and Lenses - Combination of Thin Lenses in Contact

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 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 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 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?

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.

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.

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?