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As shown in figure, a plano-convex lens ...

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.

A

20 cm

B

30 cm

C

40 cm

D

10 cm

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
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]
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