Problem 1 - College Physics

Question

\(\cdot\) A candle 4.85 \(\mathrm{cm}\) tall is 39.2 \(\mathrm{cm}\) to the left of a plane mirror. Where is the image formed by the mirror, and what is the height of this image?

Step-by-Step Solution

Answer

The image is 39.2 cm behind the mirror, with a height of 4.85 cm.

Step 1: Understanding the Mirror Reflection

In the context of a plane mirror, the image formed is a virtual image. This means the distance of the image from the mirror is the same as the distance of the object from the mirror.

Step 2: Calculate Image Location

Since the candle is placed 39.2 cm to the left of the mirror, the image will also be 39.2 cm to the right of the mirror (behind the mirror).

Step 3: Height of the Image

In a plane mirror, the height of the image is the same as the height of the object. This means the height of the image will be 4.85 cm.

Key Concepts

Image Formation

A plane mirror creates images through the process of reflection. When you place an object, like a candle, in front of a plane mirror, light rays bounce off the object and hit the mirror. These reflected rays then travel to your eyes, and your brain processes them to create an image.

In the context of plane mirrors, the image appears to be the same distance behind the mirror as the object is in front of it. This means if an object is placed 39.2 cm from the mirror, the image will also appear 39.2 cm behind the mirror. The line joining the object and its image passes through a point on the mirror that is exactly midway between them.

The image formed by a plane mirror has special characteristics that set it apart from images formed by curved mirrors or lenses. Understanding these characteristics is essential to grasp the concept of image formation thoroughly.

Virtual Image

One of the fascinating aspects of plane mirrors is the type of image they form, known as a virtual image. Unlike a real image, which can be projected on a screen, a virtual image cannot be captured directly because it does not actually exist at the location where it appears to be.

In virtual image formation, the light rays seem to diverge from a point behind the mirror, even though they do not actually converge there. Your brain interprets these diverging rays as if they were coming from a real point behind the mirror. Thus, you "see" an image located behind the mirror.

An easy way to understand a virtual image is to think of your own reflection. When you stand in front of a bathroom mirror, your reflection appears to be behind the mirror, yet when you reach out, there's just flat glass. This basic, yet important concept of virtual images is crucial for understanding how plane mirrors operate.

Reflection

Reflection is the fundamental principle that allows mirrors to create images. In a plane mirror, this process follows the law of reflection, which states that the angle at which incoming light hits the mirror (angle of incidence) equals the angle at which it is reflected off (angle of reflection). This predictability allows for consistent and precise image formation.

Plane mirrors produce clear and accurate reflections because the mirror's surface is flat. This flatness ensures uniform reflection across the entire surface, which is not the case with curved mirrors that can distort images.

As the light reflects off the mirror surface, it seems to travel in straight lines. This creates a reflection that makes the image appear life-like, undistorted, and located behind the actual mirror plane. Understanding reflection is key to mastering how a plane mirror operates, as it provides the basis for how images are perceived by our eyes.

Height of the Image

The height of the image formed by a plane mirror is identical to the height of the object. This means if you have a candle that is 4.85 cm tall in front of a plane mirror, the image of the candle formed by the mirror will also be 4.85 cm tall.

This equality in height occurs because the mirror reflects the image proportionately. No magnification or reduction in size occurs in a plane mirror. Thus, the image maintains the same dimensions as the original object.

This property is especially useful when considering proportions in reflections. Mirrors are often used in design and scientific applications where maintaining the exact size and shape of an object in its reflection is crucial.