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How many images of an object will be formed when the object is placed between two plane mirrors which are inclined at the following angles to one another?
(a) \[120^\circ \]
(b) \[45^\circ \]
(c) \[180^\circ \]
(d) \[60^\circ \]
(e) \[90^\circ \]

Last updated date: 24th Jul 2024
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Hint:Plane mirrors do not produce images. They'll redirect a picture that would have developed anyway. If rays hit a second mirror after being reflected from the first, the image created by the first mirror will serve as an object for the second mirror, and this process will repeat for each subsequent reflection.

Complete step by step answer:
A mirror with a smooth reflective surface is known as a plane mirror. The angle of reflection equals the angle of incidence for light rays striking a plane mirror. The angle of incidence is an angle formed by the incident ray and the surface normal, which is an imaginary line that runs parallel to the surface. A collimated beam of light does not spread out after reflection from a plane mirror, except for diffraction effects, and the angle of reflection is the angle between the reflected ray and the normal.

The number of images produced by two adjacent plane mirrors is determined by their angle. The formula for calculating the number of images formed between two plane mirrors is:
\[n = \dfrac{{360^\circ }}{\theta } - 1\]
Where \[\theta \] denotes the angle between the mirrors.

In the question, it is given five different angles between two plane mirrors which are inclined to form the images of an object. That is,
(a) \[\theta = 120^\circ \]
Now, we are substituting the value in the formula.
Therefore we got
\[n = \dfrac{{360^\circ }}{{120^\circ }} - 1 = 3 - 1 = 2\] images.
We are repeating the same procedure for the rest of the angles too.

(b) \[\theta = 45^\circ \]
After substituting,
\[n = \dfrac{{360^\circ }}{{45^\circ }} - 1 = 8 - 1 = 7\] images.

(c) \[\theta = 180^\circ \]
We are applying the formula as like other angles,
\[n = \dfrac{{360^\circ }}{{180^\circ }} - 1 = 2 - 1 = 1\] images.

(d) \[\theta = 60^\circ \]
After substituting, we got,
\[n = \dfrac{{360^\circ }}{{60^\circ }} - 1 = 6 - 1 = 5\] images.

(e) \[\theta = 90^\circ \]
Substituting the value in the formula, that is,
\[n = \dfrac{{360^\circ }}{{90^\circ }} - 1 = 4 - 1 = 3\] images.
As the image created in one mirror becomes the object for the other mirror, the number of images increases as the angle between the mirrors decreases.

Note: Remember the formula \[n = \dfrac{{360^\circ }}{\theta } - 1\] . We can calculate the number of images produced by substituting different angles between two inclined mirrors in the formula.