Question

A spherical polished ball is used as a diverging mirror with the focal length of -20 cm a bird 25 cm tall standing 50 cm away looks directly at the mirror what are the size and position of the birds image

Answer 1

In order to find the position of the image, we can use the formula below:

`(1)/(f)=(1)/(d_o)+(1)/(d_i)`

Where f is the focal length, do is the object distance and di is the image distance.

So, using f = -0.2 meters and do = 0.50 meters, we have:

`\begin{gathered} (1)/(-0.2)=(1)/(0.5)+(1)/(d_i)\\ \\ -5=2+(1)/(d_i)\\ \\ (1)/(d_i)=-7\\ \\ d_i=-(1)/(7)=-0.1429\text{ m} \end{gathered}`

Therefore the image is located at -14.29 cm from the mirror.

Now, to calculate the size of the image, we can use the formula below:

`\begin{gathered} (-d_i)/(d_o)=(h_i)/(h_o)\\ \\ (-(-0.1429))/(0.50)=(h_i)/(0.25)\\ \\ 0.1429=2h_i\\ \\ h_i=0.07145\text{ m}=7.145\text{ cm} \end{gathered}`

Therefore the image size is 7.145 cm.