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One face of an equiconvex lens of focal ...

One face of an equiconvex lens of focal length 60cm made of glass `(mu=1.5)` is silvered. Does it behave like a convex mirror or concave mirror? Determine its focal length.

Text Solution

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Let x be the radius of curvalue of each surface.
`1/60 =(1.5-1)[1/x -1/(-x)]` or, `1/60xx0.5xx2/x implies x=60cm`
Let ‘f ’ be the focal length of the equivalent spherical mirror, Then
`1/f =1/f_(1) + 1/f_(m) + 1/f_(1)` or, `1/f=2/f_(10 -1/f_(m)`
Here `f_(1) = +60cm`(convex lens)
`f_(m)=R/2=-30cm therefore1/f=2/60+1/30=2/30`
`impliesf=+15cm`
The positive sign indicates that the resulting mirror is convex.
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