The radius of curvature of the convex face of a plano-convex lens is `12` cm and its refractive index is `1.5` (a)Find the focal length of this lens.The plane surface of the lens is now silvered.(b)At what distance from the lens will parallel rays incident on the convex face converge?(c)Sketch the ray diagram to locate the image,when a point object is placed on the axis `20 cm`from the lens (d)Calculate the image distance when the object is placed as in (c).

Explanation

(a) `(1)/(f_1)=((3)/(2)-1)((1)/(12)-(1)/(infty))=(1)/(24)impliesf_1=24cm`
(b) Equivalent focal length of silvered lens
`(1)/(F)=(1)/(f_l)+(1)/(f_m)+(1)/(f_l)=(2)/(f_l)+(1)/(f_m)=(2)/(24)+(1)/(infty)=(1)/(12)`
The silvered lens will behave as concave mirror.
The rays will converge at foces of concave mirror i.e., At distance 12 cm from mirror/silvered lens.
(c)
(d) `u=-20cm,f=-12cm,v=?`
`(1)/(v)+(1)/(u)=(1)/(f)`
`(1)/(v)+(1)/(-20)=(1)/(-12)`
`(1)/(v)=(1)/(-12)+(1)/(20)=(-5+3)/(60)`
`v=-30cm`
Distance of image from silvered lens/concave mirror is 30 cm.