The graph shows how the magnification m produced by a thin lens varies with image distance v. What is the focal length of the lens used?

A ray of light AO in vacuum is incident on a glass slab at angle 60° and refracted at angle 30° along OB as shown in the figure. The optical path length of light ray from A to B is:

One plano-convex and one plano-concave lens of same radius of curvature 'R' but of different materials are joined side by side as shown in the figure. If the refractive index of the material of 1 is $$\mu $$₁ and that of 2 is $$\mu $$₂, then the focal length of the combination is :

A convex lens of focal length 20 cm produces images of the same magnification 2 when an object is kept at two distances x₁ and x₂ (x₁ > x₂) from the lens. The ratio of x₁ and x₂ is :-