Question

A kid had a coin and wanted to perform a trick with it as mentioned.
Case 1: He wanted to get 5 virtual images of the coin.
Case 2: He wanted to get 3 virtual images of the coin.
In both cases, how many minimum numbers of plane mirrors have to be used and what should be the
orientation of the mirrors (angles between them).​

Answer 1

Answer:

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answer is (i)

Explanation:

Answer 2

Answer:

The minimum number of mirrors are $2$ and orientation are $60^{0}$ and $90^{0}$.

Explanation:

• A virtual image cannot be obtained on a screen.
• A plane mirror gives a virtual image of an object.
• The number of virtual images depends on the angle of orientation between two plane mirrors.

Relation between the number of images and orientation angle is given by:

$n=(\frac{360}{\alpha })-1$     if   $(\frac{360}{\alpha } )$  is even.

  $=(\frac{360}{\alpha })$           if  $(\frac{360}{\alpha } )$  is odd.

where, $\alpha$ is the angle between the mirrors.

            $n$ is the number of images.

Step 1:

Case 1:  If $5$ virtual images have to be formed then applying formula:

$5=(\frac{360}{\alpha })-1$

$\alpha =\frac{360}{6}$ $degrees$

$\alpha =60$ $degrees$

So, the orientation of mirrors $=60$ $degrees$

Step 2:

Case 2:  If $3$ virtual images have to be formed then applying formula:

$3=(\frac{360}{\alpha })-1$

$\alpha =\frac{360}{4}$ $degrees$

$\alpha =90$ $degrees$

So, the orientation of mirrors $=90$ $degrees$

Hence, correct option is Case 1: $2$ mirrors and $60^{0}$ , Case 2: $2$ mirrors and $90^{0}$.