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Question: To get \[9\] multiple images the angle between the plane mirrors should be:...

To get 99 multiple images the angle between the plane mirrors should be:

Explanation

Solution

Students experiment to see whether the number of reflected images increases or decreases as the angle between two mirrors is increased or decreased. There is also a connection between the size of the angles and the number of visible edges of the mirrors.
A plane mirror has a reflective surface that is flat (planar). The angle of reflection equals the angle of incidence for light rays striking a plane mirror. The angle of incidence is the angle formed by the incident ray and the normal of the surface (an imaginary line perpendicular to the surface).

Complete step-by-step solution:
Multiple images are created when two mirrors are held at an angle and an object is positioned in between the mirrors due to reflection from one mirror to the other. The angle between the two mirrors determines how many images of the object are created.
The number of images formed between two plane mirrors inclined at an angle θ to each other is given by the formula, n=360θ−1n = \dfrac{{360}}{\theta } - 1.
Case 1: when 360θ\dfrac{{360}}{\theta } is an even integer then number of the image formed, n=360θ−1n = \dfrac{{360}}{\theta } - 1
Case 2: if 360θ\dfrac{{360}}{\theta } is an odd integer and object is kept symmetrically
Then a number of the image formed, n=360θ−1n = \dfrac{{360}}{\theta } - 1 and if the object is kept asymmetrically then the number of images formed, n=360θn = \dfrac{{360}}{\theta }.
Let's assume that the object is kept as symmetrically.
Then, the number of the image formed, n=360θ−1n = \dfrac{{360}}{\theta } - 1
⇒9=360θ−1\Rightarrow 9 = \dfrac{{360}}{\theta } - 1
⇒9+1=360θ\Rightarrow 9 + 1 = \dfrac{{360}}{\theta }
Answer isθ=36∘\theta = 36^\circ

Note: When two plane mirrors are placed at a 9090 -degree angle, the first mirror's image is mirrored in the second mirror, reversing the reversed mirror image and revealing the true image. When the angle between the two mirrors is 180180 degrees, they behave as one mirror, allowing only one image to be visible. The candles, as well as the mirrors themselves, were imaged in one another as the angle between them decreased.