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

Shown in the Fig. is a shperical 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 distant object
` u=infty`
`implies mu/v - 1/oo = (mu-1)/R`
`implies v = (muR)/(mu-1) = (1.5R)/(1.5-1) =3R`
Due to presence of the plane mirror, the image formed at I behaves as a virtual object for the plane mirror & a real image I’ is formed in front of the plane mirror, at the pole P.
`implies x+x=v`
`x = v/2 =(3R)/2 = 1.5R`
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