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Shown in the Fig. is a spherical surface...

Shown in the Fig. is a spherical surface of radius of curvature R and R.I. `(=n)1.5`. Find the distance of the silvering of the plane surface so as to form an image at the pole due to a very far object.

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Since light comes from very far object
`u=oorArr(n)/(v)-(1)/(oo)=(n-1)/(R)rArrv=(nR)/(n-1)=(1.5R)/(1.5-1)=3R`
Due to presence of the plane mirror, the image found at `I` behave as a virtual object for the plane mirror & a real image `I^(')` is formed in front of the plane mirror, at the pole P.
`rArrx+x=v`
`rArr x=(v)/(2)=(3R)/(2) rArr x= 1.5R`
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