Question 150: Ray Optics

Question

Two objects A and B are placed at 15 cm and 25 cm from the pole in front of a concave mirror having radius of curvature 40 cm. The distance between images formed by the mirror is _______________.

Accepted Answer

Using Mirror formula
$$
\begin{aligned}
& \frac{1}{v}+\frac{1}{u}=\frac{1}{f} \\
& \frac{1}{v}=\frac{1}{f}-\frac{1}{f} \\
& v=\frac{u f}{u-f}
\end{aligned}
$$
For object $\mathrm{A}, \mathrm{u}_{\mathrm{i}}=-15 \mathrm{~cm}, \mathrm{f}=-20 \mathrm{~cm}, \mathrm{~v}_1=$ ?
$$
\begin{aligned}
& \mathrm{v}_1=\frac{\mathrm{u}_1 \mathrm{f}}{\mathrm{u}_1-\mathrm{f}}=\frac{(-15)(-20)}{(-15)-(20)}=\frac{+300}{5} \\
& \mathrm{v}_1=+60 \mathrm{~cm}(+ ve, virtual)

\end{aligned}
$$
For object $\mathrm{B}, \mathrm{u}_2=-25 \mathrm{~cm}, \mathrm{f}=-20 \mathrm{~cm} \mathrm{v}_2=$ ?
$$
\begin{aligned}
& \mathrm{v}_2=\frac{\mathrm{u}_2 \mathrm{f}}{\mathrm{u}_2-\mathrm{f}}=\frac{(-25)(-20)}{(-25)-(-20)}=\frac{500}{-5} \\
& \mathrm{v}_2=-100 \mathrm{~cm}(- ve, real)

\end{aligned}
$$
Hence, the distance between images formed by the mirror is,
d = 60 Ã¢ÂÂ (Ã¢ÂÂ100)
= 160 cm

Answer

60 cm

Answer

40 cm

Answer

160 cm

Answer

100 cm

Ray Optics

Two objects A and B are placed at 15 cm and 25 cm from the pole in front of a concave mirror having radius of curvature 40 cm. The distance between images formed by the mirror is _______________.

Choose the correct answer: