A converging lens and a diverging mirror are placed at a separation of 15 cm. The focal length of the lens is 25 cm and that of the mirror is 4o cm. Where should a point source be placed between the lens and the mirror so that the light, after getting reflected by the mirror and then getting transmitted by the lens, comes out parallel to the principal axis?

If the image in the mirror is formed at the focus of the converging lens, then after transmission by the lens the rays of light will go parallel.


Distance between convex lens and convex mirror is 15cm


Focal length of lens, f_1 = 25cm


Focal length of the mirror, f_2 = 40cm


Let the distance between object and mirror, u = -x cm


u = -x cm


v= 25-15 = 10cm (because focal length of the lens = 25cm)


f_1= 40cm


Using lens formula,


1/v-1/u=1/f


⇒1/x=1/10-1/40


⇒x=40/3


Hence, the object distance is 15 – 40/3 = 5/3 = 1.67 cm


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