please make sure you have the right answer. Convex mirrors are used in many stor

Question

please make sure you have the right answer. Convex mirrors are used in many stores to provide a wide angle of surveillance for a reasonable mirror size. Your summer job is at a local convenience store that uses the mirror shown in the figure below. This setup allows you (or the clerk) to survey the entire store when you are 5.9 m from the mirror. The mirror has a radius of curvature equal to 1.4 m. Assume all rays are paraxial.

(a) If a customer is 10 m from the mirror, how far from the mirror is his image?
......... cm
(b) Is the image in front of or behind the mirror?

1- behind the mirrorin

2- front of the mirror

(c) If the customer is 2 m tall, how tall is his image?
..... cm

Explanation / Answer

Here, it is given that we are using convex mirror

And Radius of curvature, R = 1.4 m = 2f

a) customer is 10 m from mirror , means object distance 'O' is 10 m and given focal length = 0.7 m

So, 1/O + 1/i = 1/f => i = (O - f)/ Of = 1.328 m = 132.8 cm

b) 2- front of the mirror since i = +ve

c) Magnification ,M = -i/O = - 1.328/10 = - 0.1328 = Image Height/Object Height

Then , Image Height = - 0.1328 x 2 = - 0.2657 m = - 26.57 cm (Real and Inverted)

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