As shown in figure, a plano-convex lens of focal length 20 cm is silvered at its plane surface and it is made reflecting, then find new focal length of system.

Options

A. 20 cm
B. 30 cm
C. 40 cm
D. 10 cm

Answer

A, C, D

Explanation

By observing path of ray it is clear that before final image I is formed,
For first refraction from curved surface `therefore(1)/(f_1)` then reflection from silvered plane surface `therefore(1)/(F_M)` and then second refraction from curved surface `therefore(1)/(f_1)`
where `f_1`= focal length of plano convex lens = 20 cm
`F_m `= focal length of plane mirror =`infty`
Now, equivalent focal length, F can be obtained as follows.
`1/F=(1)/(f_1)`[Plano convex lens]
`+(1)/(F_M)` [Plane mirror]
`+(1)/(f_1)`[Plano covex lens]
`1/F=(2)/(f_1)+(1)/(f_m)=(2)/(20)+(1)/(infty)=(1)/(10)`
`therefore`F=10 cm
[Note that here `f_1` is positive. If it was concave `f_1` would be negative]