34-1 Images and Plane Mirrors#
Prompts
Distinguish real and virtual images. Which can form on a screen? Which requires an observer?
Explain the roadway mirage: why does a pool of water appear on the road? What is actually being imaged?
Sketch a ray diagram for a plane mirror: object O, image I, object distance \(p\), image distance \(i\). Where does the image form?
For a plane mirror, derive or state the relation between \(p\) and \(i\). What sign convention is used for virtual images?
In a mirror maze with equilateral triangles, why does an apparent hallway appear? What do you actually see at the end of that hallway?
Lecture Notes#
Overview#
Image: a reproduction of an object via light.
Real image: can form on a surface (screen, card); exists even without an observer.
Virtual image: perceived where backward extensions of rays intersect; requires an observer’s visual system.
Plane mirror: forms a virtual image; object distance \(p\) and image distance \(i\) satisfy \(i = -p\) (with sign convention \(p > 0\), \(i < 0\)).
Real vs virtual images#
Type |
Where it forms |
Needs observer? |
|---|---|---|
Real |
On a surface (screen, film) |
No—image exists physically |
Virtual |
Where backward extensions of rays meet |
Yes—brain infers location |
Your visual system infers the direction and distance of objects from the rays entering your eye. For a virtual image, the rays appear to come from a location where no light actually originates (e.g., behind a mirror).
The roadway mirage#
On a hot day, a “pool of water” often appears on the road ahead—a virtual image of the sky. Light from the low sky refracts through air that is progressively warmer (and less dense) near the road. The decreasing index of refraction bends rays toward the horizontal, then upward. Your brain extends these rays backward and infers they came from the road surface. The bluish color (from sky) and shimmer (from turbulence) enhance the illusion.
Plane mirror: ray diagram and relation#
A point object O at distance \(p\) in front of a plane mirror emits rays that reflect according to the law of reflection. The backward extensions of the reflected rays intersect at a point I behind the mirror—the virtual image.
Ray tracing: From congruent triangles (e.g., perpendicular ray and one oblique ray), the image is as far behind the mirror as the object is in front:
Sign convention: Object distance \(p > 0\). For a virtual image (behind the mirror), image distance \(i < 0\). Thus:
Extended objects: Each point of the object acts as a point source. The virtual image has the same orientation and height as the object.
Important
Only a small portion of the mirror contributes to the image seen by a given eye position. The useful region is where reflected rays from the object reach the eye.
Poll: Where does Joe see the image?
Joe sees the image of a book in a plane mirror, as shown from above. Where does Joe see the image?
[FIGURE: Top view—book, mirror, Joe; four labeled positions A, B, C, D. Image is behind mirror on the perpendicular through the book, same distance as book from mirror.]
(A) A
(B) B
(C) C
(D) D
Poll: Joe moves sideways—what happens to the image?
Joe sees an image on a dotted line through the book, perpendicular to the mirror. Joe then moves sideways (as shown). Compared to its original location, the image:
(A) Doesn’t move
(B) Is at the same distance from the mirror but above the dotted line
(C) Is at the same distance but below the dotted line
(D) Stays on the dotted line but moves toward the mirror
(E) Stays on the dotted line but moves away from the mirror
Mirror maze#
In a mirror maze with walls at 60° (equilateral triangles), you may see an apparent straight hallway. A ray reflects from mirror B to mirror A and reaches your eye. Your brain extends it backward and perceives mirror B (or an image) behind A. Tracing further: the ray ultimately originates from you. What you see at the “end” of the hallway is a virtual image of yourself.
Example: Two parallel mirrors—apparent distance to back of head
You sit in a hair salon with two nearly parallel mirrors 5.0 m apart. Your head is 2.0 m from the nearer mirror. Looking toward it, you see your face and then, farther away, the back of your head. How far away does the back of your head appear to be?
Solution: First image of your face: 2.0 m behind the near mirror. First image of the back of your head: 2.0 m + 5.0 m = 7.0 m behind the near mirror (light goes to far mirror, reflects, comes back). So the back of your head appears 7.0 m away.
Summary#
Real image: forms on a surface; needs no observer. Virtual image: perceived where backward extensions of rays meet; requires observer.
Plane mirror: forms virtual image behind mirror; \(i = -p\) with \(p > 0\), \(i < 0\).
Roadway mirage: virtual image of sky caused by refraction through warm air near the road.
Mirror maze: apparent hallway is a virtual image; at the “end” you see yourself.