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A point object is placed at a distance of 12 cm on the principal axis of a convex lens of focal length 10cm. A convex mirror is placed coaxially on the other side of the lens at a distance of 10cm. If the finalimage coincides with the object, sketch the ray diagram and find the focal length of the convex mirror. |
Answer» Solution :Here FOCAL length of convex lens `f=+10`cm, distnce of object O from convex lens `u=-12`cm and distance between the lens and convex mirror M = 10cm.  In the absence of convex mirror the lens forms an image I. of GIVEN object O at distance v, whereas from lens formula `(1)/(v)-(1)/(u)=(1)/(f.)` `(1)/(v)= (1)/(f)-(1)/(u)=(1)/((10))+(1)/((-12))=(1)/(60) rArr v=60cm`. However, when mirror M is placed behind the convex lens, the light rays RETRACE their path after reflection from the mirror and final image I is formed at the position of object. It is possible only if rays FALL normally on the mirror i.e., distance `PI.=60-10=50` cm is the radius of curvature of the convex mirror. Thus, radius of curvature of given convex mirror R = 50 cm `rArr` Focal length of convex mirror `f=(R )/(2)=25cm` |
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