Question

A concave mirror of focal length 'f₁' is placed at a distance 'd' from a convex lens of focal length 'f₂'. A parallel beam of light coming from infinity parallel to principal axis falls on the convex lens and then after refraction falls on the concave mirror. If it is to retrace the path, the distance 'd' should be ______.

Options

• 2f₁ + f₂

• f₁ + f₂

• -f₁ + f₂

• 2f₁ - f₂

Answer 1

A glass slab of thickness 4 cm contains the same number of waves as in 'x' cm of water column when both are traversed by the same monochromatic light. If the refractive indices of glass and water for that light are `5/3` and `4/3` respectively, the value of x will be 2f₁ + f₂.

Explanation:

The convex lens will form image at its focus, i.e. at a distance f₂ from it. If this image falls on the centre of curvature of the concave mirror, the rays falling on it will be normal to the mirror and retrace their path.

Hence d = 2f₁ + f₂