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By means of plotting find : (a) the pa...

By means of plotting find :
(a) the path of a light ray after reflectin from a concave and convex spherical mirrors (see Fig. where `F` is the focal point, `OO'` is the optical axis) ,

(b) the positions of the mirror and its focal point in the cases illunstrated in Fig. where `P` and `P`' are the conjugate points.

Text Solution

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Look for a point `O'` on the axis such that `O P'` and `O'` make equal angles with `O'O`. This determines the position of the mirror. Draw a ray from `P` parallel to the axis. This must on reflection pass thorugh `P'`. The intersection o fthe reflected ray with principle axis determines the focus.

(b) Suppose `P` is the object and `P`' is the image. Then the mirror is convez beacuse the image is virtual, crect & diminished. Look for a point `X` (between `P` & `P`') on the axis such that `PX` and `P' X` make equal angle with the axis.
(b)
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