Question

A convex lens, of focal length, f₁ , and a convex mirror (having its centre of curvature at the point C), of focal length, f₂ , are set up as shown. It is observed that, for this set up, there is no parallex between an object, put at A, and its image, formed by the ‘combination’. The ratio of the focal length, f₁ and f₂ , is then equal, to

(1) \(\frac{d(a+x+d)}{2a(x+d)}\)

(2) \(\frac{2a(x+d)}{d(a-x-d)}\)

(3) \(\frac{2a(x+d)}{d(a+x+d)}\)

(4) \(\frac{2d(x+d)}{a(a+x+d)}\)

Answer 1

(3) \(\frac{2a(x+d)}{d(a+x+d)}\)

The image of the object, put at A, coincides with the object itself. This implies that the rays, refracted by the convex lens, are incident normally on the convex mirror. Hence the image, formed by the convex lens alone, is at a distance (x+d), from the lens. For the lens, we then have

We are given that C is the centre of curvature of the mirror.