A screen S is placed a distance b = 5 cm from a circular convex mirror as shown in Fig. An object KP of height h = 3 cm is arranged a distance a = 5 cm from the screen.
Where must an observer position himself to see the image of the entire object? What are the maximum dimensions of the object (with the given arrangement of the object, the mirror and the screen) for the mirror to reproduce an image of the entire object? The diameter of the mirror is d = 10 cm.
Text Solution
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Sol. See Fig.; h 1 = 5 cm.
If K 1 P 1 is the image of the object KP the rays forming the image of the point K will only be propagated inside the cone enclosed by the rays K 1 A and K 1 B. The rays forming the image of the point P will pass inside the cone enclosed by the rays P 1 P and P 1 C.
In order to see the entire image the observer should place his eye inside the band between the straight lines K 1 A and P 1 C in which the rays coming from all the points on the object are superposed. The maximum dimensions of the object are determined from the similarity of the triangles DES and SPR (in this case the curvature of the section DE is neglected as is common in elementary optics):
= 
, PR = h 1 = 
= 5 cm.
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