Question

The number of images formed by the combination of two mirrors is $9$. What is the angle between the two mirrors?

• A. $36°$
• B. $40°$
• C. $90°$
• D. both (a) and (b)

Answer 1

The correct option is D

both (a) and (b)

Step 1 Given Data:

The number of images $\left(n\right)$ formed by the combination of two mirrors is $9$

Step 2: Formula Used:

1. $n=\left[\frac{360}{\theta }-1\right]$
2. $n=\left[\frac{360}{\theta }\right]$

Conditions:

1. $n=\left[\frac{360}{\theta }-1\right]$ if $\raisebox{1ex}{$360$}\!\left/ \!\raisebox{-1ex}{$\theta $}\right.$ is even
2. $n=\left[\frac{360}{\theta }\right]$ if it comes odd and when the object is placed asymmetrically.
3. $n=\left[\frac{360}{\theta }-1\right]$ when $\raisebox{1ex}{$360$}\!\left/ \!\raisebox{-1ex}{$\theta $}\right.$ is odd and the object is kept symmetrically.
4. $n=\left[\frac{360}{\theta }\right]$ is a fraction, then the number of images formed will be equal to its integral part.

Step 3 : Calculation:

We are given with $n=9$

1. Using the formula, $n=\left[\frac{360}{\theta }-1\right]$ we get,
   $$\begin{gathered} 9=\left[\frac{360}{\theta }-1\right] \\ 9+1=\frac{360}{\theta } \\ \theta =\frac{360}{10} \\ \theta =36° \end{gathered}$$
2. And, using the formula, $n=\left[\frac{360}{\theta }\right]$ we get,
   $$\begin{gathered} 9=\frac{360}{\theta } \\ \theta =\frac{360}{9} \\ \theta =40° \end{gathered}$$

Hence, Option (D) is correct. Both (a) and (b), $n=36°and40°$