Question

7. A spherical polished metallic ball is used as a diverging mirror (f = -20 cm) over a birdbath. Abird, 25 cm tall, standing 50 cm away, looks directly at the mirror. What are the size and position of the birds image

Answer 1

Given:

f = -20 cm

height, h = 25 cm

distance = 50 cm

Let's find the size and position of the birds image.

Apply the formula:

`(1)/(f)=(1)/(v)+(1)/(u)`

Where:

f = -20 cm

u = - 50 cm

Rewrite the formula and solve for v.

`\begin{gathered} (1)/(v)=(1)/(f)-(1)/(u) \\ \\ (1)/(v)=(1)/(20)-(1)/(-50) \\ \\ (1)/(v)=(1)/(20)+(1)/(50) \\ \\ (1)/(v)=(5+2)/(100) \\ \\ (1)/(v)=(7)/(100) \\ \\ v=(100)/(7)=14.28\text{ m/s} \end{gathered}`

Now, let's find the height of the image:

`\begin{gathered} (h_i)/(h_o)=(-v)/(u) \\ \\ (hi)/(25)=(-14.28)/(-50) \\ \\ hi=(14.28*25)/(50) \\ \\ h_i=7.14\text{ cm} \end{gathered}`

We can see the image height is smaller.

The formed image is virtual and erect.

ANSWER:

• The image height is smaller.

,

• The formed image is virtual and erect.