Question

An object placed in front of a concave mirror of radius 20 cm produces an inverted image which is one-fifth the size of the object. How far is the object from the mirror?
30 cm
40 cm
50 cm
60 cm

Answer 1

Answer on Question #52728-Physics-Optics

An object placed in front of a concave mirror of radius 20 cm produces an inverted image which is one-fifth the size of the object. How far is the object from the mirror?

30 cm

40 cm

50 cm

60 cm

Solution

We know

$$\frac{1}{d_o} + \frac{1}{d_i} = \frac{1}{f}.$$

Magnification is

$$M = -\frac{d_i}{d_o} = -\frac{1}{5}.$$

Thus,

$$d_i = \frac{d_o}{5}.$$

So,

$$\frac{1}{d_o} + \frac{1}{\frac{d_o}{5}} = \frac{1}{f} \rightarrow \frac{6}{d_0} = \frac{1}{f}.$$ $$d_0 = 6f = 6\frac{R}{2} = 3R = 3 \cdot 20 \text{ cm} = 60 \text{ cm}.$$

Answer: 60 cm.

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