E. Physics: Light and Geometric Optics · Light and Geometric OpticsImages in Plane Mirrors
E2.3 E3.3 E2.1 A1.5 A1.8About 70 minutes
Learning goals- I can explain how a plane mirror forms a virtual image.
- I can describe any image using SALT: size, attitude, location and type.
- I can locate the image of an object in a plane mirror with perpendicular distances and with a ray diagram.
- I can explain how a periscope works.
Words to know
image
A likeness of an object formed by reflected or refracted light.
virtual image
An image formed where light rays only appear to come from; it cannot be projected onto a screen.
real image
An image formed where light rays actually meet; it can be projected onto a screen.
SALT
Size, Attitude, Location, Type: the four characteristics used to describe an image.
attitude
Whether an image is upright or inverted.
lateral inversion
The apparent left-right reversal of an image in a plane mirror.
periscope
A device that uses two parallel mirrors (or prisms) at 45° to let you see over or around obstacles.
Who is that in the mirror?
Every morning you look into a bathroom mirror and see someone who looks exactly like you, standing behind the glass. But nobody is back there, and no light comes from behind the wall. So where is the image, and why does it seem to be there?
In this lesson you will learn how a plane mirror forms an image, how to locate that image with a ray diagram, and how to describe any image using four characteristics.
How we see an image
Light from a point on an object spreads out in all directions. Some rays hit the mirror and reflect (θi = θr) into your eye. Your brain assumes light always travels in straight lines, so it traces the reflected rays straight back. They all seem to come from one point behind the mirror. That point is the image.
No light actually passes through the image point behind the mirror. The rays only appear to come from there. An image like this is a virtual image: you can see it, but you cannot project it onto a screen. (A real image is formed where light rays actually meet; you can catch it on a screen. You will meet real images with curved mirrors and lenses.)
Describing an image: SALT
Scientists describe every image with four characteristics. Remember them with SALT:
- S – Size: is the image larger, smaller or the same size as the object?
- A – Attitude: is the image upright or inverted (upside down)?
- L – Location: where is the image? (Its distance from the mirror, and which side.)
- T – Type: is the image real or virtual?
For a plane mirror, the image is always:
- S: the same size as the object,
- A: upright,
- L: the same distance behind the mirror as the object is in front, on a line perpendicular to the mirror,
- T: virtual.
The image also shows lateral inversion: left and right appear swapped. Raise your right hand and your image raises the hand on its left. That is why the word on the front of many ambulances is printed backwards: drivers ahead read it correctly in their mirrors.
Two ways to locate an image
Method 1: Perpendicular distances (fast). For each important point on the object (for an arrow: the tip and the tail):
- Draw a dashed line from the point to the mirror, perpendicular to the mirror.
- Measure the distance and continue the line the same distance behind the mirror.
- Mark the image point. Join the image points with a dashed line (dashed because the image is virtual).
Method 2: Ray diagram (shows why). From one object point, draw two rays to the mirror. At each point of incidence, draw the normal and the reflected ray using θi = θr. Extend the reflected rays backwards behind the mirror with dashed lines. Where they cross is the image point.
Worked exampleExample 1: Moving towards a mirror
Maya stands 2.5 m in front of a plane mirror. (a) How far is she from her image? (b) She walks 0.5 m towards the mirror. How far is she from her image now? (c) Use SALT to describe her image.
- (a) Her image is 2.5 m behind the mirror. Distance from Maya to her image = 2.5 m + 2.5 m = 5.0 m.
- (b) Now she is 2.5 − 0.5 = 2.0 m from the mirror, and so is her image. Distance = 2.0 m + 2.0 m = 4.0 m.
- Notice: she moved 0.5 m, but the gap between her and her image shrank by 1.0 m, because the image also moved 0.5 m towards the mirror.
- (c) S: same size; A: upright; L: 2.0 m behind the mirror; T: virtual.
(a) 5.0 m, (b) 4.0 m, (c) same size, upright, 2.0 m behind the mirror, virtual.
Worked exampleExample 2: Let's draw a ray diagram for a point object
A small LED is 3.0 cm in front of a plane mirror. Show with a ray diagram where the image is, and where an eye must be to see it.
- Draw the mirror as a line with hatching on the back. Mark the LED (O) 3.0 cm in front.
- Draw ray 1 from O to the mirror. Draw its normal and its reflected ray with θr = θi.
- Draw ray 2 from O to a different point on the mirror, and reflect it the same way.
- Extend both reflected rays backwards with dashed lines. They cross 3.0 cm behind the mirror, on the perpendicular through O: that is the image (I).
- Any eye that receives the reflected rays (in front of the mirror, in the region the rays travel through) sees the LED's image at I.
The image is 3.0 cm behind the mirror, directly opposite the LED, and it is virtual.
A plane-mirror technology: the periscope
A periscope uses two parallel plane mirrors, each at 45° to the tube. Light from an object above enters the top opening, hits the top mirror with θi = 45°, and turns through 90°. It travels down the tube, hits the bottom mirror, turns 90° again, and leaves towards the viewer's eye. Submarine crews, tank crews and people in a crowd at a parade all use periscopes to see over obstacles. (Many modern periscopes use prisms instead of mirrors; you will see why in the lesson on total internal reflection.)
Drawing tips for plane mirrors
- Draw the mirror as a line with short hatch marks on the back (non-reflecting) side.
- Use a ruler for every ray and a protractor or set square for normals and perpendiculars.
- Real rays are solid with arrows; extensions behind the mirror and virtual images are dashed.
- Check your diagram: is the image the same distance behind the mirror as the object is in front?
Just for funRiddle: I copy everything you do, I always stand exactly as far behind the glass as you stand in front of it, and you can never shake my hand. What am I?
Your virtual image (there is nothing really there to touch).
Hands-on activityFind the image without a mirror (well, almost)
You need: a clear plastic or glass pane from a picture frame (it acts like a weak mirror and is also see-through), two identical objects (such as two identical erasers, game pieces or batteries), modelling clay, a ruler, paper and a pencil. For the extension: two small mirrors (with taped edges) and a coin.
- Draw a line across the paper. Stand the pane upright on the line with modelling clay.
- Put object 1 about 8 cm in front of the pane. Looking into the pane, you will see a faint reflection of object 1.
- Place object 2 behind the pane. Move it until it seems to sit exactly where the reflection is, even when you move your head from side to side. (When they stay lined up as you move your head, there is no parallax: object 2 is at the image location.)
- Mark both positions and measure each distance to the line. Repeat for two other distances.
- Record do and di in a table. What do you conclude?
Extension: stand two small mirrors on their edges, touching, at an angle of 90°, then 60°, then 45°. Count the images of a coin placed between them. Compare with N = 360° ÷ θ − 1.
What to look for: di = do within a few millimetres. At 90° you see 3 images, at 60° you see 5, and at 45° you see 7.
Safety (grown-up note): Picture-frame glass can have sharp edges: cover the edges with tape or use a plastic pane.
Your turn
1Describe the image in a plane mirror using SALT.
Same size, upright, same distance behind the mirror as the object is in front, virtual.
2What is the difference between a real image and a virtual image?
A real image forms where light rays actually meet and can be projected onto a screen. A virtual image forms where rays only appear to come from; it cannot be projected.
3A cat sits 1.2 m in front of a mirror. How far is the cat from its image?
Image is 1.2 m behind the mirror, so the distance is 1.2 + 1.2 = 2.4 m.
4What is lateral inversion? Give an example.
Left and right appear swapped in a mirror image. Example: your raised right hand looks like a left hand in the mirror; "AMBULANCE" printed backwards reads correctly in a rear-view mirror.
5Why is a virtual image drawn with dashed lines?
Because no light actually reaches that location; the dashed lines show where the rays only appear to come from.
6How many images do you see of an object between two mirrors at 60°?
N = 360° ÷ 60° − 1 = 5 images.
More practice: warm-up
1What does the A in SALT stand for?
Attitude: upright or inverted.
2Is the image in a plane mirror upright or inverted?
3An object is 30 cm from a plane mirror. Where is the image?
4How many mirrors does a simple periscope use, and at what angle?
Two mirrors, each at 45°.
5Can you project a plane-mirror image onto a screen?
No: it is a virtual image.
More practice: on your own
1Liam walks towards a mirror at 1.0 m/s. How fast does he approach his image?
His image also moves towards the mirror at 1.0 m/s, so they approach each other at 2.0 m/s.
2Explain, using rays, why your image seems to be behind the mirror.
Reflected rays reach your eye from the mirror. Your brain traces them back in straight lines, and the lines meet at a point behind the mirror, so the image appears there.
3A ruler stands 15 cm in front of a mirror, perpendicular to the floor. Its top is 30 cm high. Where is the image of the top of the ruler?
15 cm behind the mirror and 30 cm high: directly opposite the top of the ruler, on a perpendicular to the mirror.
4Why do you need two rays to locate an image point in a ray diagram?
The image is where the reflected rays (extended backwards) intersect. One line alone does not give an intersection point; two lines cross at one point.
5In a periscope, at what angle of incidence does light strike each mirror, and what is the total change in direction after both mirrors?
θi = 45° at each mirror; each turns the light through 90°, and the two turns are in opposite senses, so the light leaves travelling in its original direction, just lower.
Challenge
1Ana is 1.70 m tall, and her eyes are 1.60 m above the floor. What is the shortest plane mirror on a wall in which she can see her whole body, and where must its bottom edge be?
The ray from her feet reflects into her eyes at the point halfway between eye and feet: 0.80 m above the floor (bottom edge). The ray from the top of her head reflects at halfway between head and eyes: (1.70 + 1.60) ÷ 2 = 1.65 m. Mirror length = 1.65 − 0.80 = 0.85 m: half her height.
2Does the minimum mirror length in the previous question depend on how far Ana stands from the mirror? Explain.
No. The reflection points are always halfway (in height) between her eyes and her feet or head, because of θi = θr and similar triangles. Distance from the mirror does not change those heights.
3Two mirrors meet at 90°. Explain why you see 3 images of a coin, not 2.
Each mirror forms one image (2 images). Each of those images is also reflected in the other mirror; for 90° those two second reflections land on the same spot, giving one extra image. Total: 2 + 1 = 3 (N = 360° ÷ 90° − 1 = 3).
Quiz
1. The image in a plane mirror is:
2. An object is 40 cm in front of a plane mirror. The distance between the object and its image is:
3. What does the T in SALT stand for?
4. Why is the word AMBULANCE printed backwards on the front of some ambulances?
6. How many images are formed by two mirrors at 45° to each other?
Big idea: Expectations E2.3 and E3.3 ask students to predict and describe image characteristics. SALT (Size, Attitude, Location, Type) is the checklist they will use for every mirror and lens in the unit, so it is worth memorizing now.
Common difficulties:
- Thinking the image is "on" the mirror surface. It is behind the mirror, as far behind as the object is in front.
- Real vs virtual. A real image can be caught on a screen; a virtual image cannot. Plane mirrors only make virtual images.
- Drawing. Rays must be ruled and must obey θi = θr. Extensions and virtual images are dashed.
How to help: Stand with your teen in front of a full-length mirror and walk towards it together. Ask them to predict how the distance to their image changes. Try the two-mirrors-at-an-angle extension: it is a quick way to check the formula. Tape any sharp glass edges.