Question 222: Ray Optics

Question

Distance between object and its image (magnified by $-\frac{1}{3}$ ) is 30 cm . The focal length of the mirror used is $\left(\frac{x}{4}\right) \mathrm{cm}$,
where magnitude of value of $x$ is _________.

Accepted Answer

$$\begin{aligned}
&\begin{aligned}
& M=-\frac{1}{3} \
& -\frac{-V}{-U}=\frac{-1}{3} \Rightarrow V=\frac{U}{3}
\end{aligned}\
&	ext { Distance b/w object and image : }
\end{aligned}$$
$$\begin{aligned}
& U-V=30 \
& U-\frac{\mu}{3}=30 \
& \Rightarrow U=45 \quad V=15 \
& \frac{1}{f}=\frac{1}{V}+\frac{1}{U}=-\frac{1}{15}-\frac{1}{45} \
& \Rightarrow F=\frac{45}{4} \
& x=45
\end{aligned}$$

Ray Optics

Distance between object and its image (magnified by -\frac{1}{3} ) is 30 cm . The focal length of the mirror used is \left(\frac{x}{4}\right) \mathrm{cm}, where magnitude of value of x is _________.

Integer / Numeric Answer Type