A boy in a barber's shop sits between two parallel mirrors. The number of images observed by him will be

Analysis

The question asks for the number of images formed when an object (the boy) is placed between two plane mirrors that are positioned parallel to each other.

Concept Explanation

When two plane mirrors are placed parallel to each other (at an angle of $\theta = 0^\circ$), light rays reflect back and forth between the two surfaces. Each reflection creates a new image of the previous image.

The formula for the number of images ($n$) formed by two plane mirrors inclined at an angle $\theta$ is:

In this scenario, since the mirrors are parallel, the angle between them is $0^\circ$. Substituting this into the formula:

Mathematically, division by zero is undefined, which in physical optics implies that the reflections continue indefinitely. As the light bounces between the two parallel surfaces, it creates an infinite series of images that get progressively fainter.

Step-by-Step Solution

1. Identify the setup: The mirrors are parallel, meaning the angle between them is $0^\circ$.
2. Apply the principle: Because the mirrors are parallel, light rays are trapped in a cycle of infinite reflections.
3. Conclusion: Each reflection produces an image, and because the reflections never cease, the number of images formed is infinite.

Identify the Answer

The correct option is A.

Exam Tip

Whenever you see a question about mirrors at an angle, remember:

• Parallel mirrors ($0^\circ$): Infinite images.
• Perpendicular mirrors ($90^\circ$): $\frac{360}{90} - 1 = 3$ images.
• General rule: If the result of $\frac{360}{\theta}$ is an even number, the number of images is $\frac{360}{\theta} - 1$. If it is an odd number, the number of images is $\frac{360}{\theta} - 1$ (if the object is off-center) or $\frac{360}{\theta}$ (if the object is exactly on the bisector).