To get three images of a single object, the angle between the two plane mirrors should be
To get three images of a single object, the angle between the two plane mirrors should be
$50^{\circ}$
$60^{\circ}$
$72^{\circ}$
$90^{\circ}$
Solution
As the object is placed symmetrically, $\mathrm{n}=\left(\frac{360^{\circ}}{\theta}-1\right) \Rightarrow 3=\left(\frac{360^{\circ}}{\theta}-1\right) \Rightarrow \theta=90^{\circ}$
Alternative Solution:
This question is about the concept of multiple images formed by two plane mirrors arranged at an angle.
We know that the number of images formed by two plane mirrors inclined at an angle $\theta$ can be calculated by using the formula $360^{\circ}/\theta$. If the result is a whole number, the number of images is one less than this whole number. If the result is not a whole number, then it equals the number of images.
So to find the correct angle for three images, we need an angle such that when we divide $360^{\circ}$ by that angle, we get a number slightly greater than 3.
Checking the options:
A) $360^{\circ}/50^{\circ} = 7.2$, which is greater than 3 but not slightly greater.
B) $360^{\circ}/60^{\circ} = 6$, which is greater than 3 but again not slightly greater.
C) $360^{\circ}/72^{\circ} = 5$, still not slightly greater than 3.
D) $360^{\circ}/90^{\circ} = 4$, which is just one more than 3.
Therefore, the correct answer is D) $90^{\circ}$, because when we divide $360^{\circ}$ by $90^{\circ}$, we get an integer that is one more than the number of images we desire.