Problem 43 - University Physics with Modern Physics

Question

Suppose your height is \(2.0 \mathrm{~m}\) and you are standing \(50 \mathrm{~cm}\) in front of a plane mirror. a) What is the image distance? b) What is the image height? c) Is the image inverted or upright? d) Is the image real or virtual?

Step-by-Step Solution

Answer

Question: A person is standing 50 cm in front of a plane mirror with a height of 2.0 meters. Determine the image distance, image height, if the image is inverted or upright, and if it is real or virtual. Answer: The image distance is 50 cm, image height is 2.0 meters or 200 cm, the image is upright, and it is a virtual image.

Step 1: Determine the image distance

In a plane mirror, the image distance is always equal to the object distance. The person is standing 50 cm in front of the mirror, so the image distance is 50 cm.

Step 2: Determine the image height

In a plane mirror, the image height is always equal to the object height. The person's height is 2.0 meters or 200 cm, so the image height is also 2.0 meters or 200 cm.

Step 3: Determine if the image is inverted or upright

In a plane mirror, the image is always upright. This means the image is not inverted.

Step 4: Determine if the image is real or virtual

In a plane mirror, the image is always virtual. A virtual image is formed when the light rays appear to converge after reflection, but do not actually converge in physical space. A real image, on the other hand, is one where the light rays actually converge after reflection. In the case of a plane mirror, the image appears to be behind the mirror, so it is virtual.

Key Concepts

Image Distance

Understanding the concept of image distance is essential when studying reflections in plane mirrors. Image distance refers to how far the image appears to be from the mirror surface. In a plane mirror, the image distance is an interesting characteristic because it's always equal to the object distance. This means if you stand 50 centimeters away from the mirror, like in the textbook exercise, your image appears exactly 50 centimeters behind the mirror surface. This one-to-one correspondence makes drawing ray diagrams and visualizing image formation straightforward.

• The image distance equals the object distance.
• The property is always true for plane mirrors.

Keep in mind, even though we measure the image distance from the mirror, we perceive it as being 'behind' the mirror, contributing to the 3D effect we experience when looking at reflections.

Image Height

The image height in a plane mirror is another straightforward concept to understand. The height of the image produced will be the same as the height of the object. For example, if you stand at 2 meters tall in front of a plane mirror, your reflection will appear to be 2 meters tall as well. This is because plane mirrors produce images with a 1:1 scale.

• Image height is equal to object height.
• Reflections in a plane mirror are at full scale, with no magnification or reduction.

Therefore, when you look into a plane mirror, the size of the image you see always matches your actual size, offering a true reflection without any distortion in height.

Inverted vs Upright Image

When differentiating between inverted and upright images, plane mirrors are known to produce images that are always upright relative to the object. Unlike images formed by lenses or curved mirrors which can be inverted, the reflection in a plane mirror maintains the same orientation as the object.

• In a plane mirror, the image is always upright.
• There is no inversion of the image from head to toe.

This characteristic is particularly intriguing since it's a key reason why mirrors are so useful in everyday life; they show us a view of ourselves and our surroundings that is the right way up, providing a representation that matches our real-world experience.

Real vs Virtual Image

The distinction between real and virtual images is fundamental in the study of optics. Real images are those where light rays actually converge, while virtual images are locations from which light rays appear to come but do not actually converge. For plane mirrors,

• The image is always virtual.
• Light rays only appear to come from behind the mirror but do not actually converge there.

In our textbook exercise, this feature means that although your reflection seems to be behind the mirror's surface, there is no actual convergence of light there. It's like an illusion where your brain interprets the light rays as if they were emanating from a real object behind the mirror, even though it's just a reflection.