Conceptual Physics

What is the angle of reflection?

Same as angle of incidence: 25°

31.6 - Ray diagrams for planar mirrors

In this section, we use ray diagrams to explore some properties of an image produced by a planar mirror. To review these: The image created by a planar mirror is virtual, upright (right side up), the same distance from the mirror as the object, and the same size as the object. Using the ray diagram in Concept 1, we first show why the image is virtual. You see two rays emanating from a point on the penguin’s head. They reflect off the mirror and travel to the eye of an observer viewing the penguin’s image. In this diagram, we are not concerned with what the penguin sees. We are using him as an object whose image is being viewed by an observer. Because the observer’s brain assumes that light travels in a straight line, it projects an image behind the mirror. Dashed lines, called virtual rays, show the paths the brain presumes are followed by rays emanating from the source of the light. The brain locates the top of the image at the point where these virtual rays converge. Since this point is behind the mirror, and no light actually comes from it, it forms part of a virtual image.

Rays also emanate from a point on the penguin’s foot and reflect from a lower point on the mirror back to the observer’s eye. The observer’s brain locates the bottom of the image at a point where the virtual extensions of those rays intersect, a point behind the mirror and below the location of the image’s head. This confirms that the image is not only virtual, but upright as well. The diagram in Concept 2 shows that the image is the same distance behind the mirror as the object is in front. The two colored triangles share a common side (the mirror) and two pairs of equal angles, including a pair of right angles. This means the triangles are congruent, so their bottom legs must have equal lengths, and di and do must have equal magnitudes. A similar argument with two other congruent triangles demonstrates that the image has the same height as the object.

Ray diagram

Draw rays using law of reflection Find image location with virtual rays

To relate object, image distances

Draw a ray Identify equal angles Congruent triangles prove object, image distances have same magnitude

31.7 - Spherical mirrors

Spherical mirror: A mirror

that is a portion of a sphere.

Concave mirror: A curved

mirror whose reflective side

is on the inside of the curve.

Concave and convex spherical mirrors.