Question

A concave mirror has a focal length of 6cm. An object with a height of 0.6m is placed 10cm away from it. Calculate:
i) Image distance.
ii) Image height.

Answer 1

Dear Student ,
Here in this case the given data is ,
focal length f = 6 cm , object distance = u = 10 cm .object height = 0.6 m .
Let us take that the image distance is v .
Now from the equation of spherical mirror we get ,
$$\begin{gathered} \frac{1}{v}+\frac{1}{u}=\frac{1}{f} \\ \Rightarrow \frac{1}{v}=\frac{1}{f}-\frac{1}{u} \\ \Rightarrow \frac{1}{v}=\frac{1}{6}-\frac{1}{10}=\frac{5-3}{30} \\ \Rightarrow \frac{1}{v}=\frac{2}{30}=\frac{1}{15} \\ \Rightarrow v=15cm \\ Nowasthemagnificationoftheconcavemirroris, \\ m=\frac{f}{u-f}=\frac{6}{10-6}=\frac{6}{4}=\frac{3}{2} \\ Nowagainthemagnificationism=\frac{imageheight}{objectheight} \\ Therefore,imageheight=magnification\times objectheight=\frac{3}{2}\times 0·6=0·9m \end{gathered}$$
Regards