A flat mirror that is 0.85 m tall is nailed to a wall so that its upper edge is 1.7 m above the

step 1 So here we're going to have a person, could be you, could be me, right, whose height is 1 .7 met

A flat mirror that is 0.85 m tall is nailed to a wall so...

A flat mirror that is $0.85 \mathrm{m}$ tall is nailed to a wall so that its upper edge is $1.7 \mathrm{m}$ above the floor. Use the law of reflection and a ray diagram to determine if this mirror will show a person who is $1.7 \mathrm{m}$ tall his or her complete reflection.

Key Concepts

Law of Reflection

The law of reflection states that the angle at which an incident ray strikes a surface is equal to the angle at which it reflects away from that surface. This fundamental principle of optics is essential for understanding how light behaves when it encounters reflective surfaces, such as mirrors, and is used to determine the path of light rays in reflections.

Plane Mirrors and Virtual Images

Plane mirrors form images by reflecting light in such a way that the image appears to be the same distance behind the mirror as the object is in front of it. These images are virtual, meaning they cannot be projected on a screen, and they maintain the same size as the original object. This concept is crucial in understanding how a mirror can show the complete reflection of an object, such as a person’s body.

Mirror Geometry and Image Coverage

The relationship between the dimensions and placement of a mirror and the resulting visible image is an important concept in optics. Specifically, the mirror does not need to be as tall as the object to reflect its full image; rather, the positions of the mirror's upper and lower edges relative to the viewer’s eyes determine the range of the body that is visible in the reflection. This geometric reasoning helps in determining whether a mirror of a given height and placement will capture a complete reflection.

Ray Diagrams in Reflection

Ray diagrams are a visual tool used in physics to map the paths that light rays take when they reflect off a surface. By drawing the incident and reflected rays in relation to the normal at the point of reflection, one can predict the position and size of the reflected image. This method is instrumental for analyzing mirror problems and ensuring that the reflected image meets certain conditions, such as covering the entire body of a person.

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