Question

A Plane mirror produces a magnification of (A) 0 (B) \(+1\) (C) \(-1\) (D) \(\infty\)

Short answer

(B) \(+1\)

Step-by-step solution

Answer

(B) \(+1\)

Key concepts

Magnification

Magnification is a key concept in optics that describes how much larger or smaller an image appears compared to the actual object. In the case of plane mirrors, the magnification is always +1. This means the image produced is the same size as the object. The formula to express magnification is given by:
\[ m = \frac{h_i}{h_o} \]
where \( h_i \) is the height of the image and \( h_o \) is the height of the object. For plane mirrors:

• The object distance is equal to the image distance.
• The height of the image equals the height of the object (\( h_i = h_o \)).

So, when looking into a plane mirror, you will see a life-sized reflection of yourself or any object placed in front of it.This consistency makes plane mirrors useful in everyday applications like grooming mirrors, interior decorations, and periscopes.

Reflection

Reflection is the phenomenon where light bounces off a surface. In the context of plane mirrors, reflection obeys the laws of reflection. These are:

• The angle of incidence is equal to the angle of reflection.
• The incident ray, the reflected ray, and the normal to the surface all lie in the same plane.

A plane mirror reflects light in a predictable pattern, which is why the image appears upright and is the same size as the object. Because the light path is reversible, if you change your position relative to the mirror, the image appears to move, maintaining the same lateral positioning.Transformations: - The image is laterally inverted, swapping left and right sides. - However, vertical orientation remains unchanged. Examples of this can be observed when writing on paper and observing how letters appear reversed in the mirror.

Optics

Optics is the branch of physics that studies light and its interactions. Plane mirrors are a fundamental topic within optics. They demonstrate basic principles of image formation, which are also applicable to more complex optical devices:

• A plane mirror forms virtual images, meaning the image cannot be projected on a screen.
• Understanding plane mirrors helps us grasp concepts of real and virtual images seen in curved mirrors or lenses.

Applications of plane mirrors in optics include periscopes and kaleidoscopes, which use multiple reflections to achieve desired effects. The simple yet precise laws governing plane mirrors provide foundational knowledge that is built upon in complex optical systems such as cameras, telescopes, and microscopes. Optics reveals how plane mirrors integrate into daily practical tools and scientific instruments alike. This integration emphasizes the importance of mastering basic optical principles to explore advanced technological applications.