Two identical glass ($$\mu $$_g = 3/2) equiconvex lenses of focal length $$f$$ each are kept in contact. The space between the two lenses is filled with water $$\left( {{\mu _w} = 4/3} \right)$$. The focal length of the combination is

An air bubble in a glass slab with refractive index 1.5 (near normal incidence) is 5 cm deep when viewed from one surface and 3 cm deep when viewed from the opposite face. The thickness (in cm) of the slab is

Match the corresponding entries of column 1 with column 2. [Where m is the magnification produced by the mirror]

Column 1			Column 2
(A)	m = - 2		(p)	Convex mirror
(B)	m = -$${1 \over 2}$$		(q)	Concave mirror
(C)	m = +2		(r)	Real image
(D)	m = +$${1 \over 2}$$		(s)	Virtual image

A astronomical telescope has objective and eyepiece of focal lengths 40 cm and 4 cm respectively. To view an object 200 cm away from the objective, the lenses must be separated by a distance