Answer to Question #90421 in Optics for Shalom atah

Question

An object 7m high is placed 15cm from a concave spherical mirror of radius 245cm .describe the image

Answer 1

Mirror focal distance:

$$F=\frac{R}{2} = \frac{2.45}{2}=1.225 m$$

Because of $u<F$ , where $u$ - distance from mirror to object and $v$ - distance from image to mirror, then:

$$\frac{1}{u}-\frac{1}{v}=\frac{1}{F}$$

and

$$v = \frac{Fu}{F-u} = \frac{1.225 \times 0.15}{1.225-0.15} = 0.17 m$$

The height of the object is:

$$y'=y\frac{v}{u}=7\times \frac{0.17}{0.15}=7.98 m$$

Thus, the image will be imaginary, enlarged, with a height of 7.98 m, at a distance of 0.17 m behind the mirror.