A glass tumbler having inner depth of 17.5 cm is kept on a table. A student starts pouring water ($$\mu$$ = 4/3) into it while looking at the surface of water from the above. When he feels that the tumbler is half filled, he stops pouring water. Up to what height, the tumbler is actually filled?

An object is placed at the focus of concave lens having focal length f. What is the magnification and distance of the image from the optical centre of the lens?

Two plane mirrors M₁ and M₂ are at right angle to each other shown. A point source 'P' is placed at 'a' and '2a' meter away from M₁ and M₂ respectively. The shortest distance between the images thus formed is : (Take $$\sqrt 5 $$ = 2.3)

Curved surfaces of a plano-convex lens of refractive index $$\mu$$₁ and a plano-concave lens of refractive index $$\mu$$₂ have equal radius of curvature as shown in figure. Find the ratio of radius of curvature to the focal length of the combined lenses.