A convex spherical mirror forms a virtual image 0.52 times the size of the object. The distance between object and image is 14.4 cm. How do you find magnitude of the radius of curvature of the mirror????
We use the lens eqn 1/s + 1/s’ = 2/R where s is the object distance and s’ is the image distance
also the magnification m = s’/s so s’ =m*s = 0.52*s
For a virtual image s’ is negative
Since the distance between s & s’ = 14.4cm we have 0.52s + s = 14.4=> s = 14.4/1.52 = 9.47cm
and s’ = -0.52*9.47 = -4.93cm
So 2/R = 1/9.47 + 1/(-4.93) = -0.0974
So the magnitude of R = 2/0.0974 = 20.5cm
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