Question

A concave mirror has a focal length of 20 cm. Where is the image located when the object is placed 60 cm from the mirror?

15 cm in front
30 cm in front
60 cm in front
15 cm at the back

Answer 1

Answer on Question 52734, Physics, Optics

Question:

A concave mirror has a focal length of $20\mathrm{cm}$. Where is the image located when the object is placed $60\mathrm{cm}$ from the mirror?

a) $15\mathrm{cm}$ in front

b) $30\mathrm{cm}$ in front

c) $60\mathrm{cm}$ in front

d) $15\mathrm{cm}$ at the back

Solution:

Let's use the mirror equation:

$$\frac {1}{d _ {i m a g e}} + \frac {1}{d _ {o b j e c t}} = \frac {1}{f},$$ $$\frac {1}{d _ {i m a g e}} + \frac {1}{6 0 c m} = \frac {1}{2 0 c m},$$ $$\frac {1}{d _ {i m a g e}} = \frac {1}{2 0 c m} - \frac {1}{6 0 c m} = \frac {2}{6 0 c m} = \frac {1}{3 0 c m},$$ $$d _ {i m a g e} = 3 0 \mathrm{cm}.$$

The positive sign of $d_{image}$ indicate that the image is located in front of the concave mirror.

Answer:

b) $30\mathrm{cm}$ in front

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