Images in Plane Mirrors and Inclined Mirrors – Rectilinear Propagation of Light (Senior 1 Physics) | Ganzaa

Rectilinear Propagation of Light

Lessons

Senior 1 · Physics

Rectilinear Propagation of Light

5 lessons

Lesson 5 of 5

Images in Plane Mirrors and Inclined Mirrors

25 min

Where is the person in the mirror?

In a barber's kiosk in Nyabugogo, the customer faces a large mirror, and the barber holds a small mirror behind his head to show him the back. The customer sees his own face as if it were behind the glass, the back of his head somewhere further back still, and, where two mirrors meet at an angle, several copies of himself. Every one of these images can be found with the law of reflection from lesson 4 and a ruler.

Locating the image

Figure 5.1: Rays from the candle reflect into the eye. The brain assumes light travels in straight lines, so it traces the rays back (dashed) to a point behind the mirror: the image.

Each ray from the candle obeys $i = r$ at the mirror. When the reflected rays enter the eye, they seem to come from one point behind the mirror, where the dashed lines meet. No light actually passes through that point: the rays only APPEAR to come from it. An image like this is a virtual image, and it cannot be caught on a screen. Measuring shows that the image is exactly as far behind the mirror as the object is in front, on the same normal.

Important

Activity: finding an image with a candle. Stand a sheet of clear glass upright on a table (it reflects like a weak mirror but lets you see through it). Put a lit candle in front of it and move an unlit candle behind the glass until it seems to be lit by the reflected flame. Measure both distances from the glass: they are equal. Keep hair and paper away from the flame.

Definition

The image formed by a plane mirror is:

virtual: it cannot be formed on a screen;
upright: the right way up;
the same size as the object;
as far behind the mirror as the object is in front ( $v = u$ ), on the same normal;
laterally inverted: left and right are swapped.

Property	Plane-mirror image	Pinhole-camera image (lesson 3)
real or virtual	virtual	real
upright or inverted	upright	inverted
size	same as the object	depends on $\frac{v}{u}$
where it is	behind the mirror, $v = u$	on the screen
left and right	swapped (lateral inversion)	swapped

Lateral inversion

Figure 5.2: Lateral inversion. Raise your right hand in front of a mirror, and your image raises the hand on ITS left.

Worked example 1: how far away is the image?

Uwase stands $1.5\,\mathrm{m}$ in front of a plane mirror. (a) How far is her image from the mirror? (b) How far is she from her image? (c) She walks $0.5\,\mathrm{m}$ towards the mirror. How far is she from her image now?

(a) $v = u = 1.5\,\mathrm{m}$ behind the mirror.

(b) $1.5 + 1.5 = 3.0\,\mathrm{m}$ .

(c) She is now $1.0\,\mathrm{m}$ from the mirror, and so is her image: $1.0 + 1.0 = 2.0\,\mathrm{m}$ . Walking $0.5\,\mathrm{m}$ brought her $1.0\,\mathrm{m}$ closer to her image.

Worked example 2: a moving image

Mugisha walks straight towards a mirror at $1.0\,\mathrm{m\,s^{-1}}$ . How fast does his image approach him?

Each second he gets $1.0\,\mathrm{m}$ closer to the mirror, and so does his image, from the other side. The gap between them shrinks by $2 \times 1.0 = 2.0\,\mathrm{m}$ each second: the image approaches him at $2.0\,\mathrm{m\,s^{-1}}$ .

Two mirrors at an angle

Figure 5.3: Two mirrors at 90°. Each mirror forms an image of O, and each image forms an image in the other mirror, but those two land at the same point, I₃. Three images in all.

Light from the object can reflect once from either mirror, or from one mirror and then the other, so images of images appear. The smaller the angle $\theta$ between the mirrors, the more images. For an object between the mirrors:

n = \frac{360^\circ}{\theta} - 1

Angle between the mirrors $\theta$	180°	90°	60°	45°	36°	30°	0° (parallel)
Number of images $n$	1	3	5	7	9	11	endless (in theory)

The formula gives the exact number when $\frac{360^\circ}{\theta}$ is an even whole number, as in the table. When it is odd (for example $\theta = 72^\circ$ or $120^\circ$ ), it gives the count for an object placed halfway between the mirrors; an object off that line can show one image more. With parallel mirrors, as in some salons and lifts, each image is reflected again and again, making a long row of images that fade into the distance.

Worked example 3: counting the images

Two plane mirrors are inclined at $60^\circ$ to each other, with a coin between them. How many images of the coin are formed?

n = \frac{360^\circ}{60^\circ} - 1 = 6 - 1 = 5

Together with the coin itself, you see six coins arranged in a circle.

Worked example 4: finding the angle

At what angle must two mirrors be set to form 7 images of an object between them?

7 = \frac{360^\circ}{\theta} - 1 \quad\Rightarrow\quad \frac{360^\circ}{\theta} = 8 \quad\Rightarrow\quad \theta = \frac{360^\circ}{8} = 45^\circ

Warning

Common mistakes. (1) Measuring the image distance from the OBSERVER instead of from the mirror. (2) Forgetting the " $- 1$ " in $n = \frac{360^\circ}{\theta} - 1$ : the object itself is not an image. (3) Calling a plane-mirror image real: no light passes through the place where it appears, so it is virtual and cannot be caught on a screen.

Tip

Plane-mirror image in five words: virtual, upright, same size, same distance, laterally inverted. To draw it, go along the normal from the object, through the mirror, the same distance out the other side.

Mirrors at work

Plane mirrors let a barber show a customer the back of his head, let a tailor's customer see a whole outfit, and make a small shop or salon look twice as big. Two mirrors at $45^\circ$ to the line of sight make the periscope of lesson 4, and the kaleidoscope sold as a toy uses mirrors inclined to each other to turn a few beads into a pattern.

Plane mirror image characteristics (The Physics Classroom). Watch how the image location is found with the law of reflection, and the list of properties of a plane-mirror image.

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Practice

List five properties of the image formed by a plane mirror.
Draw a ray diagram, with two rays, to show how the image of a point object in a plane mirror is formed. Mark the object and image distances.
Ishimwe stands $2.0\,\mathrm{m}$ from a mirror. How far is she from her image? She steps $0.5\,\mathrm{m}$ back. How far is she from her image now?
How many images are formed by two mirrors inclined at (a) $90^\circ$ ; (b) $45^\circ$ ; (c) $30^\circ$ ?
Two mirrors form 9 images of a candle placed between them. What is the angle between the mirrors?
Why is the word AMBULANCE painted back to front on the front of an ambulance?
Keza is $1.6\,\mathrm{m}$ tall. Using the law of reflection, explain why a wall mirror only $0.8\,\mathrm{m}$ tall, hung at the right height, is enough for her to see her whole body.

Show answersHide answers

Virtual; upright; the same size as the object; as far behind the mirror as the object is in front; laterally inverted.
Two rays from the object, each reflecting with $i = r$ ; the reflected rays traced back with dashed lines meet behind the mirror at the image, on the same normal as the object, with $v = u$ .
$2.0 + 2.0 = 4.0\,\mathrm{m}$ ; after stepping back she is $2.5\,\mathrm{m}$ from the mirror, so $2.5 + 2.5 = 5.0\,\mathrm{m}$ from her image.
(a) $\frac{360}{90} - 1 = 3$ ; (b) $\frac{360}{45} - 1 = 7$ ; (c) $\frac{360}{30} - 1 = 11$ .
$\frac{360^\circ}{\theta} = 10$ , so $\theta = 36^\circ$ .
A mirror image is laterally inverted. A driver in front sees the ambulance in the rear-view mirror, where the back-to-front word appears the right way round and can be read at once.
Light from her feet reflects into her eyes from a point on the mirror halfway (in height) between her eyes and her feet, and light from the top of her head from a point halfway between her eyes and the top of her head. The mirror only needs to span between these two points, which is half her height: $\frac{1.6}{2} = 0.8\,\mathrm{m}$ , whatever her distance from the mirror.

Key points

A plane mirror forms a virtual, upright, same-size, laterally inverted image, as far behind the mirror as the object is in front.
The image is located by tracing reflected rays back behind the mirror, each obeying $i = r$ .
Two mirrors at an angle $\theta$ form $n = \frac{360^\circ}{\theta} - 1$ images; parallel mirrors form a long row of images.

1Where is the person in the mirror?

2Locating the image

3Lateral inversion

4Two mirrors at an angle

5Mirrors at work

Where is the person in the mirror?

Locating the image

Lateral inversion

Two mirrors at an angle

Mirrors at work