A concave mirror of focal length $$f$$₁ is placed at a distance of d from a convex lens of focal length $$f$$₂. A beam of light coming from infinity and falling on this convex lens $$-$$ concave mirror combination returns to infinity. The distance d must equal

When a biconvex lens of glass having refractive index 1.47 is dipped in a liquid, it acts as a plane sheet of glass. This implies that the liquid must have refractive index

A ray of light is incident at an angle of incidence i, on one face of a prism of angle A (assumed to be small ) and emerges normally from the opposite face. If the refractive index of the prism is $$\mu $$. the angle of incidence i, is nearly equal to

A converging beam of rays is incident on a diverging lens. Having passed through the lens the rays intersect at a point 15 cm from the lens on the opposite side. If the lens is removed the point where the rays meet will move 5 cm closer to the lens. The focal length of the lens is