Notifications
Clear all
Light Reflection and Refraction
1
Posts
2
Users
0
Likes
221
Views
0
13/08/2021 1:24 pm
Topic starter
An arrow 2.5 cm high is placed at a distance of 25 cm from a diverging mirror of focal length 20 cm. Find the nature, position and size of the image formed.
1 Answer
0
13/08/2021 1:31 pm
\(h_1\) = 2.5 cm, u = -25 cm, f = 20 cm
We know that
\(\frac{1}{v}\) + \(\frac{1}{u}\) = \(\frac{1}{f}\)
⇒ \(\frac{1}{v}\) + \(\frac{1}{-25}\) = \(\frac{1}{20}\)
⇒ \(\frac{1}{v}\) =\(\frac{1}{25}\) + \(\frac{1}{20}\)
= \(\frac{4 + 5}{100}\)
= \(\frac{9}{100}\)
∴ v = \(\frac{100}{9}\) cm = 11.1 cm
The image is formed 11.1 cm behind the convex mirror.
Now,
m = -\(\frac{v}{u}\) = \(\frac{h_2}{h_1}\)
⇒ -\(\frac{11.1}{-25}\) = \(\frac{h_2}{2.5}\)
⇒ \(h_2\) = \(\)\frac{11.1 \times 2.5{25}[/latex = 1.11 cm
The image is virtual, erect and 1.11 cm tall.