a. A flat mirror is located at the focal length from the lens. Find at what distance from the lens the image of an object located at distance from the lens will be located.
b. The flat side of a flat-convex lens with a focal length of is silvered. Find the focal length of the resulting mirror.
Solution
For problem
a. If there were no mirror, the object at Point would have had an image at Point at the distance to the right of the lens (according to the thin lens equation). Instead, the mirror reflects light rays converging to Point B to Point C at the distance
to the left of the lens (assuming no refraction by the lens at the moment). Instead, the lens refracts light rays converging to Point to Point at the distance to the left of the lens, where
As a reality check, when , we have ; that is, light rays from the object becomes parallel to the principal axis after emerging from the lens and will return to the location of the object after reflection by the mirror and another refraction by the lens. Note that if any of the "distance" is negative, then the point is on the opposite side of the instrument to what is indicated; for example, a point at a negative distance to the left of the lens is on the right of the lens. This convention makes the solution valid in every possible scenario.
b. After the flat side of a planoconvex lens with focal length is silvered, the new instrument has focal length equal to that of a biconvex lens, because the reflected light rays behave symmetrically to those going through the biconvex lens.
Discussion
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