Question

A convex mirror has a radius of 20 cm. An object is placed 30 cm in front of the mirror. Determine where the image will appear.

−4.5cm

−5.5cm

−6.5cm

−7.5cm

Answer 1

Answer on Question 52380, Physics, Optics

Question:

A convex mirror has a radius of $20\mathrm{cm}$. An object is placed $30\mathrm{cm}$ in front of the mirror. Determine where the image will appear.

a) $-4.5\mathrm{cm}$

b) $-5.5\mathrm{cm}$

c) $-6.5\mathrm{cm}$

d) $-7.5\mathrm{cm}$

Solution:

Let's first find the focal length of the convex mirror. By the definition, the focal length of the curved mirror is half a radius of curvature:

$$f = \frac {R}{2} = \frac {20\mathrm{cm}}{2} = 10\mathrm{cm}.$$

Then, from the mirror equation we have:

$$\frac {1}{d _ {i m a g e}} + \frac {1}{d _ {o b j e c t}} = \frac {1}{- f},$$ $$\frac {1}{d _ {i m a g e}} + \frac {1}{30\mathrm{cm}} = \frac {1}{- 10\mathrm{cm}},$$ $$\frac {1}{d _ {i m a g e}} = - \frac {1}{10\mathrm{cm}} - \frac {1}{30\mathrm{cm}} = - \frac {4}{30\mathrm{cm}} = - \frac {2}{15\mathrm{cm}} = - \frac {1}{7.5\mathrm{cm}},$$ $$d _ {i m a g e} = - 7.5\mathrm{cm}.$$

The negative sign of $d_{image}$ indicate that image is located behind the convex mirror.

Answer:

d) $-7.5\mathrm{cm}$

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