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

The magnifying power of a telescope is 9. When it is adjusted for parallel rays the distance between the objective and eyepiece is 20 cm. The focal length of lenses are

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

A thin prism of angle 15^o made of glass of refractive index $$\mu $$₁ = 1.5 is combined with another prism of glass of refractive index $$\mu $$₂ = 1.75. The combination of the prisms produces dispersion without deviation. The angle of the second prism should be