Plane Mirrors: Videos & Practice Problems
Plane Mirrors form images because light scattered from an object reflects from the mirror and enters the eye. In a ray diagram, reflected rays are traced backward to the place they appear to come from, producing a virtual image behind the mirror. This image is seen by the eye, but it does not form on a screen in front of the mirror.
The key relationship is that the object distance and image distance have equal magnitude: \(d_O=-d_I\) . This means the image is the same distance behind the mirror as the object is in front. A plane-mirror image is upright, same size as the object, and reversed from right to left rather than upside down. Its magnification is \(M=1\) .
Understanding ray diagrams, the law of reflection, and these image properties helps with geometry-based optics problems involving positions, distances, and reflected views in flat mirrors.
Ray Diagrams for Plane Mirrors
A candle is placed in front of a plane mirror. Which of the following diagrams correctly shows the image?
Ray Diagrams for Plane Mirrors Example 1
Here's what students ask on this topic:
In a plane mirror, the object distance () and the image distance () have equal magnitude but opposite signs. This means the image appears the same distance behind the mirror as the object is in front of it. Mathematically, this is expressed as . The negative sign indicates that the image is virtual and located behind the mirror surface. This relationship is fundamental in ray diagrams and helps us understand how virtual images are formed in plane mirrors.
Images in plane mirrors appear reversed from right to left due to the way light rays reflect off the mirror surface. When you raise your right hand, the mirror reflects the light rays such that the image appears to raise its left hand. However, the image remains upright because the vertical orientation is preserved by the reflection. This lateral inversion happens because the mirror reverses the front-back direction, making the image appear as if it is inside the mirror, but it does not flip the image vertically. This is why your reflection is upright but laterally inverted.
Ray diagrams help locate the image formed by a plane mirror by tracing light rays from the object to the mirror and then reflecting them according to the law of reflection. Typically, two or three rays are drawn from the top of the object: one ray strikes the mirror perpendicularly and reflects back on itself, and another ray strikes the mirror at an angle and reflects with the same angle. By extending the reflected rays backward behind the mirror, they appear to converge at a point where the virtual image is formed. This point is the same distance behind the mirror as the object is in front, allowing us to visualize the image's position and size.
Images formed by plane mirrors have several key properties: (1) The image is virtual, meaning it cannot be projected onto a screen and appears behind the mirror. (2) The image is upright, maintaining the same vertical orientation as the object. (3) The image is laterally inverted, reversed from right to left. (4) The size of the image is the same as the object, so the magnification () is equal to one, . (5) The image distance equals the object distance in magnitude but is located behind the mirror, expressed as . These properties are essential for understanding reflections in plane mirrors.
To calculate the distance between points on an object and its image in a plane mirror, you use the fact that the image is the same distance behind the mirror as the object is in front. For example, if a meter stick is placed 30 cm in front of the mirror, the image will appear 30 cm behind it. To find the distance between two points, such as the 50 cm mark on the object and the mirror image of the 40 cm mark, you add the distances along the line: the distance from the 50 cm mark to the mirror, the distance from the mirror to the image of the 40 cm mark, and the difference between the points on the object. This approach uses basic geometry and the relationship to find the total distance.
