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The image of an object, formed by a com...

The image of an object, formed by a combination of a convex lens (of focal length f) and a convex mirror (of radius of curvature R), set up as shown is observed to coincide with the object.

Redraw this diagram to mark on it the position of the centre of the mirror. Obtain the expression for R in terms of the distances, marked as a and d, and the focal lenght f, of the convex lens.

Text Solution

Verified by Experts

`u=-a,v=d+R`
Using lens formula
`(1)/(d+R)-(1)/(-a)=(1)/(f)`
`(1)/(d+R)=(1)/(f)-(1)/(a)=(a-f)/(fa)`
`impliesd+R=(fa)/(a-f)impliesR=(fa)/(a-f)-d`
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