A thin equi-convex `(mu = (3)/(2))` lens of focal length 10 cm is cut and separated. A material of `mu = (5)/(2)` is introduced between between them. The flat portion of one of the part is silvered as shown in figure. The focal length of new combination is

Options

A. `-10cm`
B. `-10//4cm`
C. `-10//3cm`
D. None of these

Answer

c.

Explanation

`(1)/(f)=(mu-1)((1)/(R_(1))-(1)/(R_(2)))`
`R=10cm`
`f^(')=(3-1)((1)/(-10)-(1)/(10))`
`f^(')=(-10)/(4)`
`(1)/(f_(eq))=(1)/(20)-(4)/(10)+(1)/(20)=(2)/(20)-(4)/(10)`
`f_(eq)=-10//3cm`