Answer to Question #200393 in Optics for Piolo

Question

An object of height 3.0 cm is placed at 5.0 cm in front of a diverging lens of focal length 20 cm and observed from the other side. Where and how large is the image?

di = _____ cm

hi = ______ m

answer to the nearest 1 decimal place

Answer 1

Using lens formula

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$ ....(1)

u(object distance)=-5cm

f(focus)=20cm

H_o(height of object)=3cm

V(image distance)=?

H_i(image height)=?

by using (1)

We have

$\frac{1}{v}-\frac{1}{(-5)}=\frac{1}{20}$

V=-6.6cm

And we also know that

M(magnification )=$\frac{-V}{U}=\frac{H_i}{H_o}$

$\implies$ putting values we get

$\frac{-(-6.6)}{-5}=\frac{H_i}{3}$

H_i=-3.96

Negative sign indicates that image is inverted