The focal length of any resulting optic device can be found by letting parallel rays from infinity (parallel to the principal axis) fall on the device and finding where the image is formed.
When the plane surface isn't silvered When parallel rays fall on the curved surface, u = - Then by the refraction formula /v - 1/(-) = (-1)/R v =R/(-1) This serves as object for refraction at the plane surface. v' = v / = R/(-1) Hence focal length of this plano convex lens = R/(-1) = 40 cm
Once the plane surface is silvered Now, when the parallel rays from infinity fall on the unsilvered surface, u = - Then by the refraction formula /v - 1/(-) = (-1)/R v =R/(-1) This serves as the object for reflection from the silvered plane surface. For the reflection at this surface, the image is formed at the same distance but on the opposite side. v' = -R/( -1) This serves as the object for the next refraction at the unsilvered curved surface. 1/v'' - /v' = (1-)/R v'' = -R/2(-1) Hence, focal length of this new optical device = R/2(-1) = 20 cm.
Moderation Team
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380
/v - 1/(-
