Question

Column I represents the angle at which two mirrors are inclined and column II represents number of images formed in the arrangement. Select the option that correctly matches the number of images formed with the arrangement for an object placed asymmetrical from the mirrors.

Column I	Column II
$\left(a\right)\theta ={60}^{\circ }$	$\left(1\right)n=1$
$\left(b\right)\theta ={40}^{\circ }$	$\left(2\right)n=3$
$\left(c\right)\theta ={90}^{\circ }$	$\left(3\right)n=5$
$\left(d\right)\theta ={180}^{\circ }$	$\left(4\right)n=9$

• A. $\left(a\right)\to \left(3\right),\left(b\right)\to \left(4\right),\left(c\right)\to \left(2\right),\left(d\right)\to \left(1\right)$
• B. $\left(a\right)\to \left(2\right),\left(b\right)\to \left(3\right),\left(c\right)\to \left(1\right),\left(d\right)\to \left(4\right)$
• C. $\left(a\right)\to \left(3\right),\left(b\right)\to \left(4\right),\left(c\right)\to \left(1\right),\left(d\right)\to \left(2\right)$
• D. $\left(a\right)\to \left(2\right),\left(b\right)\to \left(3\right),\left(c\right)\to \left(4\right),\left(d\right)\to \left(1\right)$

Answer 1

The correct option is A $\left(a\right)\to \left(3\right),\left(b\right)\to \left(4\right),\left(c\right)\to \left(2\right),\left(d\right)\to \left(1\right)$

$\left(a\right)$ When $\theta ={60}^{\circ }$
$n=\frac{{360}^{\circ }}{{60}^{\circ }}=6$ ($n$ is even)
Number of images formed $n-1=6-1=5$

$\left(b\right)$ When $\theta ={40}^{\circ }$
$n=\frac{{360}^{\circ }}{{40}^{\circ }}=9$ ($n$ is odd)
Number of images formed $n=9$

$\left(c\right)$ When $\theta ={90}^{\circ }$
$n=\frac{{360}^{\circ }}{{90}^{\circ }}=4$ ($n$ is even)
Number of images formed $n-1=4-1=3$

$\left(d\right)$ When $\theta ={180}^{\circ }$
$n=\frac{{360}^{\circ }}{{180}^{\circ }}=2$ ($n$ is even)
Number of images formed is $n-1=2-1=1$

Hence option $a$ is correct