Answer to Question #205211 in Optics for Bukky

Question

An object 7m high is placed 15cm from a convex spherical mirror of radius 45cm describe it's imagine

Answer 1

Thus, the image is virtual erect and behind the mirror.

Write the expression for the focal length of the mirror

$f=\frac{r}{2}$

Here, f is the focal length and r is the radius of curvature.

Substitute 45 cm for r in the above expression.

$f =\frac{45}{2}=22.5 \;cm$

Write the expression for the mirror formula.

$\frac{1}{v} + \frac{1}{v}= \frac{1}{f}$

Substitute -15 cm for u and 22.5 cm for f in the above expression.

$\frac{1}{v} + \frac{1}{-15}= \frac{1}{22.5} \\ v= 9 \;cm$

Write the expression for the height of the image.

$\frac{h`}{h}= \frac{-v}{u}$

Substitute 9 cm for v, -15 cm for u and 7 cm for h' in the above expression.

$\frac{h`}{7}= \frac{9}{-15} \\ h`=4.2 \;cm$

Thus, the image is 9 cm behind the mirror, it is virtual, erect and the size of image is 4.2 cm.