Understanding Images Formed by Inclined Mirrors

When two plane mirrors are placed at an angle to each other, they form multiple images of an object placed between them. The number of images formed depends on the angle between the mirrors and the position of the object (symmetrically or unsymmetrically placed).

Calculating the Number of Images

The general formula to determine the number of images is related to the value of \( n = \frac{360^\circ}{\theta} \), where \( \theta \) is the angle between the two mirrors.

In this question, the angle between the two mirrors is given as \( \theta = 72^\circ \).

Let's calculate the value of \( n \):

\( n = \frac{360^\circ}{72^\circ} \)

\( n = 5 \)

Rules for Number of Images based on n and Object Position

After calculating \( n = \frac{360^\circ}{\theta} \), the number of images formed depends on whether \( n \) is an integer, and if so, whether it's even or odd, and whether the object is placed symmetrically or unsymmetrically.

• If \( n \) is an even integer, the number of images is \( N = n - 1 \), regardless of whether the object is placed symmetrically or unsymmetrically.
• If \( n \) is an odd integer, the number of images formed depends on the object's position:
  • If the object is placed symmetrically, the number of images is \( N = n - 1 \).
  • If the object is placed unsymmetrically, the number of images is \( N = n \).
• If \( n \) is a fraction, the number of images is \( N = \text{integer part of } n \).

Applying the Rules to the Given Problem

We calculated \( n = 5 \).

\( n = 5 \) is an odd integer.

The question states that the object is placed unsymmetrically.

According to the rules for an odd integer \( n \) and an unsymmetrically placed object, the total number of images formed is \( N = n \).

Therefore, the total number of images is \( N = 5 \).

Summary of Calculation

Given:

• Angle between mirrors, \( \theta = 72^\circ \)
• Object position: Unsymmetrically placed

Calculation:

\( n = \frac{360^\circ}{\theta} = \frac{360^\circ}{72^\circ} = 5 \)

Since \( n=5 \) is an odd integer and the object is unsymmetrically placed, the number of images is \( N = n = 5 \).

Based on our calculation (\( n=5 \), odd integer) and the object's unsymmetrical position, the number of images is 5.

Revision Table: Images by Inclined Mirrors

Additional Information: Multiple Reflections

The formation of multiple images by inclined mirrors is a result of successive reflections. An image formed by one mirror acts as a virtual object for the other mirror, which then forms another image. This process continues until the images are formed outside the angle subtended by the two mirrors.

When the object is placed symmetrically, one pair of images formed by successive reflections on each mirror (like \( M1 \to M2 \) and \( M2 \to M1 \)) can coincide, leading to one fewer distinct image compared to the unsymmetrical case when \( n \) is odd.

This concept is important in understanding optical instruments and phenomena involving multiple reflections.