Question

unkown spherical mirror is used to form an erect image three times the original size for an object placed at distance 15cm from it find
1-the image position
2-the focal length
3-the kind of the mirror

Answer 1

Answer on Question #43051-Physics-Optics

Unknown spherical mirror is used to form an erect image three times the original size for an object placed at distance 15cm from it find

1-the image position

Solution

The magnification of a mirror is defined as the height of the image divided by the height of the object:

$$m = \frac {h _ {i}}{h _ {o}} = - \frac {d _ {i}}{d _ {o}}.$$

The image position is

$$d _ {i} = - 3 \cdot 1 5 \mathrm {c m} = - 4 5 \mathrm {c m}.$$

I.e. image is located at distance 45cm from the mirror on the other side of the source object.

2-the focal length

Solution

From the mirror equation

$${\frac {1}{d _ {0}}} + {\frac {1}{d _ {i}}} = {\frac {1}{f}}$$

the focal length is

$$f = \frac {1}{\frac {1}{d _ {0}} + \frac {1}{d _ {i}}} = \frac {1}{\frac {1}{1 5} + \frac {1}{- 4 5}} = 2 2. 5 \mathrm {c m}.$$

3-the kind of the mirror

Answer

The image is erect and larger than origin, that's why this is a concave spherical mirror.

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