Question

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

Answer 1

Question #32217

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?

Solution:

The position of the image defined according to the Gaussian mirror equation

$$\frac{1}{d_0} + \frac{1}{d_i} = \frac{1}{f}$$

where

$d_0$ is the object distance

$d_i$ is the image distance

$f$ is the focal length

$$d_i = \frac{f d_0}{d_0 - f}$$

The focal length is defined by the following formula:

$f = \frac{R}{2}$ where $R$ is the radius of the mirror:

$$d_i = \frac{R d_0}{2 d_0 - R}$$ $$d_i = \frac{20 \cdot 30}{2 \cdot 30 - 20} = 15 \text{ cm}$$

Answer: 15 cm.