Question

A candle 4.85 cm tall is 39.2 cm to the left of a plane mirror. Where is the image formed by the mirror, and what is the height of this image?

Short answer

The image is 39.2 cm behind the mirror and 4.85 cm tall.

Step-by-step solution

Understand the Concept of Plane Mirrors

Plane mirrors produce images that are virtual, meaning they cannot be projected on a screen, and they appear to be behind the mirror. The image formed is the same distance behind the mirror as the object is in front of it, and it is the same size as the object.

Determine the Image's Distance

Since the image is virtual and appears behind the mirror, its distance from the mirror is equal to the distance of the object in front of it. Therefore, the image is 39.2 cm behind the mirror.

Calculate the Image's Position

The object (candle) is placed 39.2 cm to the left of the mirror. The image, being the same distance behind the mirror, is also 39.2 cm behind the mirror. Therefore, the image is "to the right" of the mirror, effectively making it appear at -39.2 cm on the object side of the mirror axis if you use left as positive.

Determine the Height of the Image

In plane mirrors, the height of the image is equal to the height of the object. Given that the candle's height is 4.85 cm, the image will also have a height of 4.85 cm.

Summary of the Image Characteristics

The image of the candle is virtual, located 39.2 cm behind the plane mirror, and is erect with the same height of 4.85 cm as the candle.

Key concepts

Plane Mirrors

Plane mirrors are flat, reflective surfaces that create images with unique properties. When an object is placed in front of a plane mirror, the light reflects off the mirror's surface in such a way that it seems to form an image behind the mirror. This happens because the reflected light rays appear to diverge from a single point behind the mirror, even though they actually don't go there. Key properties of images formed by plane mirrors include:

• The images are virtual, meaning they cannot be displayed on a screen because they merely appear to be located behind the mirror.
• They are upright and have the same orientation as the object.
• The images are laterally inverted, which means left and right are switched in the image compared to the object.
• The size of the image is identical to the size of the object in both height and width.

Understanding these properties helps in solving problems related to reflections in plane mirrors, such as determining an image’s location and size.

Virtual Images

In optics, a virtual image is formed when the light rays diverge, and hence, they appear to come from behind the mirror. This is in contrast with real images, where light rays converge to form the image at a particular point. Because of this nature, virtual images cannot be projected onto a screen. When considering a plane mirror, the virtual image has some distinct features:

• The image appears at the same distance behind the mirror as the object is in front of it.
• The height and size of the virtual image are the same as that of the object.
• Sitting behind the mirror, the image is not attainable in physical space.

These characteristics make virtual images handy for understanding basic optical principles, and they are pivotal in applications like makeup mirrors and various instruments.

Image Distance

The concept of image distance in relation to plane mirrors is straightforward and involves simple geometry. The image distance is the distance from the mirror to where the image appears to be. Because of the properties of plane mirrors as discussed, this is always the same as the object distance. To determine the image distance:

• Measure the perpendicular distance from the object to the mirror. This is known as the object distance.
• Since the image forms just as far behind the mirror, set this object distance equal to the image distance.

For example, if an object, like a candle, is placed 39.2 cm from the mirror, its image will also appear 39.2 cm behind the mirror. This symmetry is a defining trait of how plane mirrors operate.

Image Size

The size of an image formed by a plane mirror is another clear aspect of its reflections. Unlike concave or convex mirrors, plane mirrors produce images that are equal in size to the actual object. Here’s what this means for images in plane mirrors:

• The height of the image is exactly the same as the height of the object. For example, if a candle is 4.85 cm tall, its image in a plane mirror will also be 4.85 cm tall.
• The ratio of the image’s dimensions to the object’s dimensions is 1:1.
• Changes in the object’s size will correspond to identical changes in the image size.

This sameness in size makes plane mirrors especially useful in applications where accurate visual representation is needed, such as in dressing rooms and optical instruments.