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Chapter 3: Mirrors
Reflection is defined as the bouncing of light off an object
When light hits off most everyday objects it scatters in all directions ā this is known as diffuse reflection , but when the surface it shines off is flat and silvered ā a plane mirror ā then it behaves in a much more predictable way. In fact, we can say two things for definite about it; these two things are known as āThe Laws of Reflection of Lightā.
Laws of Reflection of Light*
- The incident ray, the normal at the point of incidence and the reflected ray all lie on the same plane.
- The angle of incidence is equal to the angle of reflection (Ī± = Ī²).
**The image formed by a plane mirror is called a āvirtual imageā ***
Both of the following headings have the same diagram for a solution. Show how an image is formed in a Plane Mirror Show that for a Plane Mirror, the image is as far behind the mirror as the object is in front.**
Spherical Mirrors
There are two types of spherical mirror; Concave and Convex. A concave mirror ācaves inā at the centre (as you look at it), whereas a convex mirror bulges out.
Real and Virtual Images A Real Image is an image formed by the actual intersection of light rays.* A real image can be located on a screen.
A virtual image is formed by the apparent intersection of light rays. A virtual image cannot be formed on a screen (because there are no actual rays to intersect behind the mirror)
Concave Mirrors ā ray diagrams In order to find out what an image of an object will look like after reflection from a spherical mirror, we draw two or three lines following simple rules, and where these lines intersect represents the position of the image.
You should be able to draw a ray diagram showing how a concave mirror forms an image of an object which is placed (i) outside the focus ā resulting in a real image (ii) inside the focus ā resulting in a virtual image
Three Rules Parallel and focal point:* From top of object to mirror (parallel to principle axis) and back through focal point. Focal point and parallel: From top of object through focal point and back parallel to the principle axis. Centre of Curvature: From top of object to centre of curvature and back out at an equal angle
For each of the following; label the centre of curvature (C), the focal point (f), the Object and the Image. Put arrows on all rays, and state whether the image is real or virtual, upright or inverted, magnified or diminished
Object outside f
Notice that when the object is inside the focal point the light rays never intersect, but from the viewerās perspective they appear to do so behind the mirror (the viewer is to the left of the mirror in the diagrams above).
Object inside f Note A real image is always in front of the mirror and inverted. A virtual image is always behind the mirror and upright.
Uses of Concave Mirrors
**1. Searchlights
- Floodlights
- Headlights in a ca** r 4. Shaving and make-up mirrors, dentistās mirror.
For applications 1 ā 3 above the light bulb is placed at the focus; this means that all light going backwards from the bulb hits the mirror and gets reflected back out parallel to the principal axis instead of spreading out in all directions.
Point 4 ā Cosmetic mirrors; if your face/tooth inside the focus the image is magnified and upright.
Magnification*
The following diagram (which you donāt need to know) illustrates that the ratio between image height and object height is also the ratio between the image distance (v) and the image distance (v).
Mandatory Experiment To Measure the focal length of a Concave Mirror
Leaving Cert Physics Syllabus
Content Depth of Treatment Activities STS
- Laws of Reflection Demonstration using ray box or laser or other suitable method.
- Mirrors Images formed by plane and spherical mirrors.
f u v
u
v
M =
Real-is-positive sign convention. Simple exercises on mirrors by ray tracing or use of formula.
Practical uses of spherical mirrors: Concave
- Dentists
- Floodlights
- Projectors. Convex
- Supermarkets
- Driving mirrors
Experiment: Measurement of the focal length of a concave mirror
MEASUREMENT OF THE FOCAL LENGTH OF A CONCAVE MIRROR
APPARATUS: Concave mirror, screen, lamp-box with crosswire, metre stick, retort stand.
DIAGRAM
Procedure
- Place the ray-box well outside the approximate focal length.
- Move the screen until a clear inverted image of the crosswire is obtained.
- Measure the distance u from the crosswire to the mirror, using the metre stick.
- Measure the distance v from the screen to the mirror.
- Repeat this procedure for different values of u.
- Calculate the focal length of the mirror using the formula f u v
(^1) = 1 + (^1) and get an average.
- Plot a graph of 1/u against 1/v and use the intercepts to get two values for f. Then get the average of these two.
RESULTS
CONCLUSION
Using the graph we got an average value for the focal length of the mirror of 25.6 cm. From the table of data we got an average value of 24.4 cm, which was close to the value we got from the graph, suggesting that both readings are reasonably accurate.
SOURCES OF ERROR / PRECAUTIONS
- Determining when the image was in sharpest focus; repeat each time and get an average.
- Parallax error associated with measuring u and v; ensure your line of sight is at right angles to the metre stick.
- Take all measurements from the centre of the mirror.
NOTES How to find an approximate value for the focal length.
- Focus the image of a distant object onto a screen.
- Measure the distance between the mirror and the screen.
- This corresponds to an approximate value for the focal length of the mirror.
Object distance u 1/u
Image distance v 1/v
Focal Length f
When drawing the diagram it is very useful to ācheatā and put the image the same distance behind the mirror as the object is in front. This should now make the diagram a lot more accurate, and lo and behold, when youāre finished the image will be the same distance behind the mirror as the object is in front!
*The image formed by a plane mirror is called a āvirtual imageā In explaining the meaning of a virtual image textbooks give some variation of the following; āThe image in a plane mirror appears to be behind the mirror. The fact that it is not means the image is a āvirtualā mirror.ā This may sound straightforward to a physics professor, but trust me; it makes little sense to a sixteen year-old student who (if you have ever thought about it at all) would have thought that the image is in the mirror. The misconception arises because, although our brain is indeed fooled into thinking that the image is behind the mirror, we quickly come to realise as infants that there is actually nothing behind there. From then on we accept that the image is (apparently) in the mirror. This is worth a class discussion in itself to try and sort out the confusion. I have a documentary on chimpanzees where the scientist involved placed a full-length mirror against a tree and waited to see what the response would be. The first chimp to see it immediately thought there was another animal behind the mirror and poked its head around to see. When it couldnāt find anyone it became confused, but quickly tired of the puzzle and resumed its previous activities. Some students may be lucky enough to try this with a young sibling. The concept of a virtual image will also be dealt with later in the chapter, when we compare it to something called a āreal imageā. We do this a lot in physics unfortunately ā talk about something which we will only study later on (if at all). This is because so many physics concepts are interconnected. I only tell you this to reassure you that itās okay to be confused. Iām not saying that you will be any less confused at the end of two years, but at least (like the sign on the door says) youāll be confused on a higher level. This also means that some of the most confused men and women who ever lived were also the greatest scientists ā including Albert Einstein. So there.
The single greatest way to explain/demonstrate the properties of a real image is with whatās called a āMagic Mirrorā. Because itās a real image it means it sits there in mid-air. You donāt generally notice images in mid-air because the light forming the image is swamped by background light. But if you cover off this background light by using a screen then the image becomes visible. This image in turn acts like a real object in that it can be magnified further, which is how microscopes work; it really is quite impressive. If you are a teacher you need to purchase a āMirage Mirrorā ā see www.sciplus.com. for about ā¬30.
*Three Rules You could theoretically use any two out of the three rays in the exercises. I strongly recommend that you do not use the i = r ray unless you have no other option, because it can be very inaccurate (unless using a protractor, or ā like the text book ā a computer). It is also advisable to put only a very slight curvature on the mirror, or better still make the mirror a straight line while drawing the rays, and only afterwards put in a slight curvature.
u
v
M =
This formula often causes confusion: While v and u are lengths (from the mirror to the image and from the mirror to the object respectively), the above formula is actually telling us about the ration between heights. So if v is 10 cm and u is 2 cm, it means that the image length is 5 times greater than the object length, but from the magnification formula it also means that the height of the image will be 5 times greater than the height of the object. In other words, the magnification is 5.
Warning about maths questions There are only two formulae in this chapter, but they can be used in many different ways, and the sign conventions can easily result in errors being made if you forget about them. Another common mistake is to add 1/u to 1/v, but forgetting to invert the answer to get f. I also suggest working the whole sum out in the calculator, rather than trying to find lowest common denominators etc. But this does require being proficient in the use of your calculator! It is also advisable in this case to show your workings in your answer. This is so that if mess up the calculator work, at lease the examiner can see that you had the right idea. Demos Ensure that you spend time playing with concave mirrors; look at the image of a distant object; now look at an image of your own face when it is very close to the mirror ā what differences can you notice?
Use a concave mirror to form an image of a distant object on a sheet of A4 paper. Try to use a colourful object ā the colour image is impressive ā can you notice anything else about it? Use the ray-box and a slit which forms three parallel rays of light to reflect off of the mirror. What do you notice?
Archimedes is said to have focussed sunlight on to advancing ships from the harbour, using soldiers to create a large concave mirror with their shields, causing the ships to burn up in the water (itās a good story at any rate).
Lenses and mirrors: ignite paper by placing paper (ignition of bugs is not condoned!) at the focal point. This is only likely to work on a sunny day with no wind.
I have a larger mirror which, if a container of water is placed at the focal point, will cause it to boil in a surprisingly short time. You will not be able to place your hand at the focal point for even a second if there is strong sunlight!
