Understanding Image Formation by Inclined Plane Mirrors

When an object is placed between two plane mirrors that are inclined at a certain angle to each other, multiple images are formed due to successive reflections. The number of images formed depends on the angle between the two mirrors.

Calculating the Number of Images

The formula used to calculate the number of images (\(n\)) formed by two plane mirrors inclined at an angle \(\theta\) is generally given by:

\(n = \frac{360^\circ}{\theta} - 1\)

This formula is applicable when the object is placed symmetrically or asymmetrically, provided that \(\frac{360^\circ}{\theta}\) is an integer. If \(\frac{360^\circ}{\theta}\) is not an integer, the number of images is often taken as the integer part of \(\frac{360^\circ}{\theta}\), depending on the object's position, but for integer results, the formula \(\frac{360^\circ}{\theta} - 1\) is standard and represents the total distinct images visible, excluding the object itself.

Applying the Formula for 30 Degrees

In this question, the angle between the two plane mirrors is given as \(30^\circ\).

Here, \(\theta = 30^\circ\).

First, let's calculate the value of \(\frac{360^\circ}{\theta}\):

\(\frac{360^\circ}{30^\circ} = 12\)

Since 12 is an integer, we can use the formula \(n = \frac{360^\circ}{\theta} - 1\) to find the number of images.

Substituting the value into the formula:

\(n = 12 - 1\)

\(n = 11\)

Therefore, you can expect to see 11 images when an object is placed between two plane mirrors inclined at an angle of 30 degrees to each other.

Let's summarize the calculation:

The calculation confirms that 11 images are expected to be seen.