A concave mirror has a focal length of 33.0 cm. The distance between an object a

Question

A concave mirror has a focal length of 33.0 cm. The distance between an object and its image is 45.3 cm. Find the object and image distances, assuming the following.

Explanation / Answer

u+v =45.3 cm f= -33 cm f =vu/(v+u) => vu = 45.3* 33 = 1494.9 a). let the object lies x distance beyond the centre of curvature. u= -(2*33+x) = -(x+66) and, x+66 +v =45.3 => v = -(x+20.7) 1/u +1/v =1/f => -1/(x+20.7) -1/(x+66) =-1/33 => x =29.68 u =-(29.68+66) =-95.68 cm v =-(29.68+20.7) = -50.38 cm b). let the object lies at y distance from the focal point. u =-(33-y) v =-(45.3-33+y) =-(12.3+y) -1/(33-y) -1/(12.3+y) =-1/33 => y =10.35 u =-(33-10.35) = -22.65cm v =-(12.3+10.35) =22.65cm

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