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Ray Tracing: Convex & Concave Mirrors

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  • 0:00 A House of Mirrors
  • 0:27 Plane Mirrors
  • 0:57 Convex Mirrors
  • 2:37 Concave Mirrors
  • 3:56 Lesson Summary
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Lesson Transcript
Instructor: Matthew Bergstresser
There are three types of mirrors: plane, convex and concave. Convex and concave mirrors are curved. In this lesson, we will explore how to determine where images are in plane, convex and concave mirrors.

A House of Mirrors

Have you ever been to carnival or state fair where there's a house of mirrors? You go inside and there are all types of mirrors that make you look short, skinny, or don't reflect your image at all! These mirrors are all curved, and based on how they are curved, strange results can be seen. You might even see mirrors like this on display as pieces of art or on the outside of planetariums.


Multiple convex mirrors made into a globe
planetarium


Plane Mirrors

Plane mirrors only produce virtual images, which are images behind the mirror. Light rays leave the image of the object in front of the mirror, and reflect off the mirror. Imaginary lines drawn normally to the mirror show how the incident angle, or incoming angle, equals the reflected angle. The reflected rays continue behind the mirror, and where they intersect is where the image is located.


Plane mirror ray diagram
plane_mirror


Notice θ = θ' and and φ = φ'. Now, let's work with curved mirrors.

Convex Mirrors

Convex mirrors are outwardly curved mirrors. Imagine the back side of a very shiny spoon. Let's look at the important parts of any curved mirror.


Convex mirror
convex


  • The principal axis is the imaginary horizontal line through the center of the mirror.
  • The center of curvature is the radius of the curve.
  • The focal point is halfway between the mirror surface and the radius of curvature. It's the location where all the reflected light appears to be coming from.

Let's go step-by step how to draw a ray diagram.

Step 1: Draw a ray (arrow) parallel to the principal axis from a point on the object. When the ray reaches the mirror, reflect the ray away from the mirror so that it looks like it's coming from the focal point. Continue the reflected ray behind the mirror with a dotted line.


Step 1 in red
ray1


Step 2: Draw another ray from the same starting point and aim it at the focal point. When the ray reaches the mirror, reflect it away from the mirror parallel to the principal axis. Continue that parallel ray behind the mirror with a dotted line.


Step 2 in blue
ray2


Step 3: Draw another ray from the same starting point on the object aimed at the center of curvature. When it reaches the mirror, reflect it directly back along itself.


Ray 3 in green
ray3


Where the rays intersect is where the image of the black arrow is located.


The image is the smaller, vertical, black arrow, and is virtual
final_convex


All convex mirrors produce virtual images that are reduced in size. The advantage of convex mirrors is they give a wider frame of view, which is why they are used in stores for security purposes, and outside rear-view mirrors in cars. The language written on outside rear-view mirrors is, ''objects in mirror are closer than they appear.'' The car in the mirror looks small, so it might lead people to think the car is far behind them when it really isn't.

Concave Mirrors

Concave mirrors are inwardly curved mirrors. Think of the front of a shiny spoon. These mirrors have focal points and centers of curvature on the front side of the mirror.


Concave mirror
concave


Drawing a ray diagram for concave mirrors is similar to drawing them for convex mirrors.

Step 1: Ray 1 is parallel to principal axis, and reflects through the focal point.


Ray 1 in red
ray1_concave


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