Answer to Question #169953 in Optics for AA

Question

An object is 0.25 m from a concave mirror with a focal length of 0.6 m the object is 0.38 m talk.

Answer 1

Given,

Object distance (u) = 0.25m

Focal length of the concave mirror $(f)=0.6m$

Length of the object $(h_o)=0.38m$

Let position of image be at v distance from the concave mirror.

Now, applying the mirror formula,

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

Now, substituting the values,

$\frac{1}{v}=\frac{1}{f}-\frac{1}{u}$

for the concave mirror, focal length always will be negative. so

$\frac{1}{v}=\frac{1}{0.6}-\frac{1}{0.25}$

$\Rightarrow \frac{1}{v}=\frac{0.25-0.6}{0.150}$

$\Rightarrow \frac{1}{v}=\frac{-0.35}{0.15}$

$v=\frac{-3}{7}cm$

Hence the height of the image $h_i=\frac{-h_o\times v}{u}=\frac{3\times 0.38}{7}cm$

$h_i=\frac{1.14}{7}cm =0.16cm$