Question

A spherical mirror is to be used to form an image, six times as tall as an object, on a screen positioned 6.0 m from the mirror. (a) Describe the type of mirror required. The mirror is a concave mirror and it has a focal length of x Your response differs from the correct answer by more than 10%. Double check your calculations, m. (b) Where should the mirror be positioned relative to the object? The object should be m in front of the mirror.

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Answer 1

Here, magnification required = -6, negative sign implies that the image will be inverted.

b)

The right side of the mirror will be taken as positive and the left side will be negative.

In mirror magnification is given by:

m = -v/u, where v = image distance = -6 m; and u = object distance.

So, - 6 = -(-6)/u

u = -1 m

i.e, the object should be at a distance of 1 m from the front of the mirror.

a)

We know, mirror formula:

$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$

Substituting values:

$-\frac{1}{6} - \frac{1}{1} = \frac{1}{f}$

$-\frac{7}{6} = \frac{1}{f}$

So, the focal length of the concave mirror used is -0.857 m

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