Question

A security mirror used in a big showroom has radius of curvature 5
m. If a customer is standing at a distance of 20 m from the cash
counter, find the position, nature and size of the image formed in the
security mirror.​

Answer 1

Answer:  Image is formed on other side of mirror at a distance of 2.22 m  from the pole. The nature of image is Virtual, Upright and Diminished.

Explanation:

We know that in the showroom convex mirrors are used as security mirrors because they increase the range of vision.

We know that,

Focal length of convex mirror is always positive. Since given that radius of curvature of mirror is 5m.

Thus focal length of mirror = 5/2 (i.e. half or radius of curvature)

Given that customer(object) is standing at a distance of 20m from the cash counter (Since it is obvious that mirror must be placed at cash counter, ; assumed). Distance of object should be taken as negative as it is placed on same side of mirror.

Distance of object(u) = -20m

Focal length (f) = 5/2

Distance of image(v) = ?

By formula,

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}\\\;\\\frac{2}{5}=\frac{1}{v}-\frac{1}{20}\\\;\\\frac{1}{v}=\frac{1}{20}+\frac{2}{5}\\\;\\\frac{1}{v}=\frac{1+8}{20}\\\;\\\frac{1}{v}=\frac{9}{20}\\\;\\v=\frac{20}{9}\\\;\\v=2.22\;\text{m}$

Since the distance of the image from the mirror is positive, So it must be on other side of mirror with respect to object.

The image  will be smaller than actual size of customer

The image  will be smaller than actual size of customerThe nature of image is virtual, upright and diminished.

Answer 2

Answer:

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