Question

It is desired to cast the image of a lamp magnified 5 times upon a wall 4 m distant from the lamp. What kind of spherical mirror is required and what is its position?

Answer 1

Answer on Question #57876-Physics-Optics

It is desired to cast the image of a lamp magnified 5 times upon a wall 4 m distant from the lamp. What kind of spherical mirror is required and what is its position?

Solution

Here the distance between the mirror and the image:

$$d_{i} + d_{o} = 4$$

The magnification is

$$\frac{d_{i}}{d_{o}} = 5$$

So,

$$d_{i} = 5 d_{o}$$

and,

$$5 d_{o} + d_{o} = 4$$

or,

$$6 d_{o} = 4$$

Therefore

$$d_{o} = \frac{2}{3} m \text{ and } d_{i} = 3 \frac{1}{3} m.$$

So, the mirror should be put $\frac{2}{3}$ meters from the lamp and $3 \frac{1}{3}$ meters from the wall.

As the image is magnified in a wall, the mirror must be concave mirror. Convex mirrors produce smaller images.

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