Question

With an object between those, if the angle between two plane mirrors is acute, the number of images formed will be:
A. more than 3
B. less than 3
C. more than 1
D. equal to zero

Answer 1

Hint: Learn about image formation in a plane mirror. From, the mathematical expression for the number of images that can be formed in two plane mirrors if the mirrors are placed facing each other at an angle. The number of images that can form it depends on the angle between the mirror and the position of the object between the mirrors.

Formula used:
The number of images formed by two plane mirror placed at an angle is given by,
\[n = \dfrac{{{{360}^ \circ }}}{A} - 1\]
where, \[n\] is the number of images and an integer, \[A\] is the angle between the mirrors.

Complete step by step answer:
When two plane mirrors are placed making an angle with each other at an angle, the number of images formed is more than one. The number of images that can be formed depends on the angle between the mirrors and the position of the object between two mirrors.

The number of images formed by the mirrors depends on the position of the body that is placed between the mirrors. if the body is placed symmetrically between the given mirrors, the number of images formed will be,
\[n = \dfrac{{{{360}^ \circ }}}{A} - 1\]
If the body is placed asymmetrically in between the given mirrors, the number of images that can be realized will be,
\[n = \dfrac{{{{360}^ \circ }}}{A}\]
Also, if \[A\] is a fraction, then the number of images formed will be equal to its closest integer.Now, here the mirrors are kept at an acute angle so, \[\theta < {90^ \circ }\].
So, the number of images must be, \[n = \dfrac{{{{360}^ \circ }}}{\theta } - 1\]
\[n > \dfrac{{{{360}^ \circ }}}{{{{90}^ \circ }}} - 1\]
\[\therefore n > 3\]
So, if the mirrors are placed at an acute angle the number of images will be more than 3.

Hence, option A is the correct answer.

Note:Whether the object is placed asymmetrically or symmetrically the number of images formed will be always more than 3 if the object is placed in between the mirrors. In a symmetrical case the number of images formed is the minimum number of images that can be formed by the mirrors.