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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

Sagot :

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:

[tex]\frac{1}{f}=\frac{1}{v}+\frac{1}{u}[/tex]

Where:

f = -20 cm

u = - 50 cm

Rewrite the formula and solve for v.

[tex]\begin{gathered} \frac{1}{v}=\frac{1}{f}-\frac{1}{u} \\ \\ \frac{1}{v}=\frac{1}{20}-\frac{1}{-50} \\ \\ \frac{1}{v}=\frac{1}{20}+\frac{1}{50} \\ \\ \frac{1}{v}=\frac{5+2}{100} \\ \\ \frac{1}{v}=\frac{7}{100} \\ \\ v=\frac{100}{7}=14.28\text{ m/s} \end{gathered}[/tex]

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

[tex]\begin{gathered} \frac{h_i}{h_o}=\frac{-v}{u} \\ \\ \frac{hi}{25}=\frac{-14.28}{-50} \\ \\ hi=\frac{14.28*25}{50} \\ \\ h_i=7.14\text{ cm} \end{gathered}[/tex]

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.

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