A plano-convex lens `(f = 20 cm)` is silvered at plane surface. The focal length will be

Options

A. The radius of curvature of curved surface of given plano-convex lens is equal to half of radius of curvature of a surface of equiconvex lens of focal length 20cm
B. An object placed at 15cm on the axis on the convex side of silvered plano-convex lens gives rise to an image at a distance 30cm from it
C. An object placed at a distance of 20cm on the axis on the convex side of silvered plano-convex lens gives rise to an image at 40cm from it
D. Silvered plano-convex lens acts as a concave mirror of focal length 10cm.

Answer

a.,b.,d.

Explanation

For plano convex lens`(1)/(f)=((mu-1))/(R)`
For equiconvex lens `(1)/(f)=(mu-1)(2)/(R^('))`
`R=(R)/(2)` [choice (a) is correct ]
Let F be the focal length of silvered plano-convex lens
`(1)/(F)=(2(mu-1))/(R)+(1)/(oo)=(2(mu-1))/(R)`
Given `(1)/(f)=(1)/(20)=(mu-1)/(R)`
`F=10cm` ( it acts on concave mirror) [choice (d) is correct]
`(1)/(u)+(1)/(v)=(1)/(F)`
If `u=-15cm, (1)/(v)=-(1)/(10)+(1)/(15)=(-3+2)/(30)=(1)/(-30)`
`v=-30cm` [coice (b) is correct]
If `u=-20cm, (1)/(v)=(1)/(-10)+(1)/(20)=(1)/(-20)rArrv=-20cm` [choice (c) is wrong]