Problem 6 - University Physics with Modern Physics

Question

What is the magnification for a plane mirror? a) +1 c) greater than +1 b) -1 d) not defined for a plane mirror

Step-by-Step Solution

Answer

Answer: a) +1

Step 1: Identify the Concept of Magnification in a Plane Mirror

To find the magnification for a plane mirror, we need to understand that magnification is the ratio of the size of an image to the size of the object being reflected. Magnification can be determined using the formula: $$ M = \frac{h_i}{h_o} $$ Where \(M\) is the magnification, \(h_i\) is the height of the image, and \(h_o\) is the height of the object.

Step 2: Consider the Characteristics of a Plane Mirror

In a plane mirror, the image formed is always virtual, erect, and the same size as the object. Given these characteristics, we can conclude that the height of the image (\(h_i\)) is equal to the height of the object (\(h_o\)).

Step 3: Calculate the Magnification of a Plane Mirror

Since the height of the image (\(h_i\)) is equal to the height of the object (\(h_o\)) in a plane mirror, we can substitute these values into the magnification formula: $$ M = \frac{h_i}{h_o} $$ $$ M = \frac{h_o}{h_o} $$ $$ M = 1 $$

Step 4: Select the Correct Answer

The magnification for a plane mirror is found to be +1. Out of the given options, the correct answer is: a) +1

Key Concepts

Virtual Image

In the fascinating world of optics, a virtual image is an image formed by rays that appear to come from a definite location but do not actually converge there. When you look into a plane mirror, everything you see is a virtual image. This is because the light rays never actually meet behind the mirror; they merely appear to do so. The virtual image in a plane mirror is not real and cannot be projected onto a screen.

Some simple characteristics of a virtual image in a plane mirror include:

• It appears behind the mirror surface.
• It cannot be captured or touched.
• It is perceived as being the same distance behind the mirror as the object is in front of it.
• The orientation of the virtual image is upright, the same as the object.

Understanding virtual images helps explain why the magnification for a plane mirror is always +1, as the virtual image is an exact replica (in size) of the object seen in the mirror.

Image Formation

When discussing plane mirrors, image formation is vital to understand. Plane mirrors form images through the reflection of light. If you think of the mirror as a flat, reflective surface, every point on that surface reflects light according to the law of reflection: the angle of incidence equals the angle of reflection. This means that light rays reflecting off the mirror appear to diverge or come from a point behind the mirror, creating the virtual image.

Steps involved in image formation in plane mirrors can be summarized as:

• Light rays strike the mirror at certain angles.
• The rays reflect off the surface at angles equal to their incidence.
• The reflected rays appear to diverge from a point behind the mirror.

With this understanding, the clarity of image formation in plane mirrors justifies why objects appear as they do, and why their height appears the same as that of the objects themselves, thus having a magnification of +1.

Plane Mirror Characteristics

Plane mirrors have distinct characteristics that influence how images are viewed:

• Image Size: The image size is the same as the object size. If you measure the height of an object placed in front of a plane mirror, the image will match that height exactly.
• Image Orientation: The image is always upright and identical in orientation to the object. This means if you raise your right hand, the image appears to raise its left, which is a peculiar property of the reflection in plane mirrors.
• Image Distance: The distance from the mirror to the virtual image is equal to the distance from the mirror to the object. This symmetry creates the illusion of three-dimensional depth.
• Image Type: The image formed is always virtual, which means it cannot be projected on a screen, as mentioned previously.

These plane mirror characteristics are fundamental in understanding how magnification is derived in plane mirrors and supports why it always results in +1. They represent a cornerstone in optic-related curricula, providing the basis for understanding more complex mirror systems.