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Question:

You are asked to design a shaving mirror assuming that a person keeps it 10 cm from his face and views the magnified image of the face at the closest comfortable distance of 25 cm. The radius of curvature of the mirror would then be :

60 cm

30 cm

24 cm

-24 cm

Solution:

The mirror formula is given as
1/v + 1/u = 1/f.. (i)
The position of object is 10cm left of mirror and position of image is 25 + 10 = 15cm right of mirror
u = -10cm and v = 15cm
substituting values in equation (i)
1/15 + 1/-10 = 1/f
1/f = -1/30
→ f = -30cm
The radius of curvature is given as
R = 2f = -60cm