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A point object O is kept at a distance of 30cm from a convex lenx of power +4 D towards its left. It is observed that when a convex mirror is kept on the right side at a distance of 50cm from the convexlens, theimage of the object O formed by the lens-mirror combination coincides with the object itself. Calculate the focal length of the convex mirror. |
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Answer» Solution :Focal length of the CONVEX lens `= ( 1)/( P) m` `f = ( 1)/( 4) m = 25 cm` Let v be the position of the imae, I, of the object formed by the convex lens alone . We then have `(1)/( v) - ( 1)/( ( -U)) = ( 1)/( f)` `rArr (1)/(v) = ( 1)/( 25) - ( 1)/( 30) = ( 6-5)/( 150) = ( 1)/( 150)` `rArrv = 150 cm` HENCE the distance of the image (formed by the convex lens alone ) from the convex mirror would be ( 150-150) cm, i.e., 100cm. This distance is equal to the radius of the curvature of the convex mirror. Hence focal length of the convex mirror equals `100 //2`. i.e., 50 cm. `:.` Radius of the curvature of the convex mirror, `R = LI - LM ` 
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