For a concave lens of focal length f, the relation between object and image distances u and v, respectively, from its pole can best be represented by (u = v is the reference line) :

A spherical mirror is obtained as shown in the figure from a hollow glass sphere. If an object is positioned in front of the mirror, what will be the nature and magnification of the image of the object?
(Figure drawn as schematic and not to scale)

There is a small source of light at some depth below the surface of water (refractive index = $${4 \over 3}$$) in a tank of large cross sectional surface area. Neglecting any reflection from the bottom and absorption by water, percentage of light that emerges out of surface is (nearly) :
[Use the fact that surface area of a spherical cap of height h and radius of curvature r is 2$$\pi $$rh]:

The aperture diameter of a telescope is 5m. The separation between the moon and the earth is 4 × 10⁵ km. With light of wavelength of 5500 $$\mathop A\limits^o $$, the minimum separation between objects on the surface of moon, so that they are just resolved, is close to :