Problem 1 - University Physics with Modern Physics

Question

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 and 4.85 cm tall.

Step 1: Understanding the Problem

Read the problem carefully. We have a candle standing in front of a plane mirror, and we're asked to find the position and the height of the image formed by the mirror.

Step 2: Position of the Image in a Plane Mirror

In a plane mirror, the image is formed as far behind the mirror as the object is in front of it. Therefore, if the object (candle) is 39.2 cm from the mirror to the left, the image will appear 39.2 cm behind the mirror.

Step 3: Image Height in Plane Mirror

In a plane mirror, the image is of the same height as the object. Therefore, the height of the image will be the same as the height of the candle, which is 4.85 cm.

Key Concepts

Plane Mirrors

Planar or flat surfaces that reflect light well are called plane mirrors. In these mirrors, the law of reflection holds perfectly, which makes them ideal for creating simple images. Each point on the surface of a plane mirror reflects light in such a way that the angles formed with the normal (a line perpendicular to the surface) are equal. This results in images that appear to be the same distance behind the mirror as the actual object is in front.

• The surface is flat, ensuring uniform reflection properties.
• The shape ensures that light reflects symmetrically, creating predictable image locations.
• Plane mirrors are common in everyday life, found in bathrooms, vehicles, and more.

Light behaves in a straightforward manner when striking a plane mirror, leading to uncomplicated image formation often used in physics experiments.

Image Formation

Image formation in plane mirrors involves a virtual image. A virtual image is formed when light rays appear to divert from a point behind the mirror. However, the light does not actually originate from there.

• The image appears to be the same size as the object.
• The distance from the mirror to the image is identical to the distance from the object to the mirror.
• Images in plane mirrors are laterally inverted or flipped from left to right.

This concept can be seen when standing in front of a flat mirror. You observe your reflection directly in front of you, but it is as far behind the mirror as you are in front of it.

Image Height

The image height in a plane mirror is directly equal to the height of the object itself. This stems from the symmetric nature of light reflection on a flat surface. Thus, regardless of how far a candle or any object is placed from the mirror, its image will match its real size.

• Image height is consistent and unaffected by the distance from the mirror.
• This property allows for practical applications, like ensuring optical devices have accurate reflections.

For example, in this exercise, since the candle is 4.85 cm tall, the image of the candle, viewed in the plane mirror, will also be 4.85 cm tall.

Reflection

Reflection is the phenomenon where light bounces back upon hitting a surface. It follows a predictable path dictated by the angle of incidence and the angle of reflection, which are always equal. This rule is known as the Law of Reflection.

• This law ensures the predictability of images formed by plane mirrors.
• Angle of incidence (the angle made with the normal line) equals the angle of reflection.

The precise nature of reflection makes it possible for plane mirrors to generate accurate virtual images, matching the object's size. Understanding reflection is crucial for interpreting how images form and appear in mirrors as well as lenses.