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A convex lens of radii of curvature 20cm...

A convex lens of radii of curvature 20cm and 30 cm respectively. It is silvered at the surface which has smaller radius of curvature. Then it will behave as `(mu_(g) = 1.5)`

Text Solution

Verified by Experts

Here the focal length of equivalent mirror can be found by Eq. 35-22
Calculation : We know that
`(1)/(f_(1))=((n_(2))/(n_(1))-1)((1)/(R_(1))-(1)/(R_(2)))`
`=(1.5-1)((1)/(20)+(1)/(30))=0.5xx(5)/(60)`
Therefore
`f_(I)=(120)/(5)=24cm`
Also
`f_(M)=(-20)/(2)=-10cm`
From Eq. 34-22, we get
`(1)/(f_(eq))=-(2)/(f_(I))+(1)/(f_(M))`
`=-(2)/(24)+(1)/(-10)=(-60)/(11)cm`
So, this system behaves like a concave mirror of focal length `60//11cm`.
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