Ray Diagrams ­ Concave Mirror
A concave mirror is a converging mirror because parallel rays will _____________
_____________________________.
For any object, millions and millions of rays are reflected in all directions. Some of these rays hit the mirror and are reflected. All of these reflected rays obey the law of reflection ­ that is the angle of ______________ will be the equal to the ______________________ ______________________.
Because these reflected rays are altered an image will be created. If the reflected rays reunite at one location the image is said to be _____________. If the reflected rays are diverging, then our brain will trace them back to the place where we thought they originated called a __________________ image. Students can draw several rays, measure the angle of incidence and the angle of reflection for each ray to find where at least 2 reflected rays intersect OR students can trace 3 special incident rays whose reflected rays can be determined without measuring an angle.
3 Special Incident Rays
1. An incident ray which is traveling parallel to the principal axis will reflect
_________________________________________________________
2. An incident ray which travels through the focal point will reflect _________________________________________________________
3. An incident ray that travels through the centre of curvature or travels as if it passed through the centre of curvature will reflect _________________________________.
Note 1 ­ only 2 rays need to be drawn to find the location of the image. When drawing 3 incident rays, if the rays aren't carefully drawn, or if the mirror is not perfect (spherical aberration), then the 3 rays will not meet at exactly the same spot. Note 2 ­ properly label each ray diagram before you draw any rays. Important labels include the Principal Axis (PA), Centre of Curvature (____), Principal Focus ( ____) and the Vertex (____)
S.
A.
L.
T.
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Summary of the Rules for finding Images in a Concave Mirror
Draw the reflected rays in the following diagrams using the knowledge you gained from the lab with curved mirrors. State the rule you learned under each diagram.
P.A.
C
F
V
P.A.
C
V
F
An incident ray that travels through C will
An incident ray that travels through F will
An incident ray that travels parallel to the P.A.
P.A.
P.A.
C
F
V
P.A.
C
C
F
F
V
V
An incident ray that travels along the P.A.
2
For each of the following, find the image and state the characteristics of the image.
S.
A.
L.
T.
S.
A.
L.
T.
S.
A.
L.
T.
What pattern exists with the images as you move the object closer and closer to the mirror?
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S.
A.
L.
T.
S.
A.
L.
T.
What pattern exists as the object moves closer to the focal point?
S.
A.
L.
T.
S.
A.
L.
T.
What pattern exists in the last two diagrams?
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Summary of Results for a Concave Mirror
Objects placed out of F (whose distance to the vertex is greater than the focal length) will produce ________________ images.
All real images are _____________________
When the object is far from the mirror, the image is close to _____________ and the image size is __________________
As the object moves closer to the mirror, the image ____________________ and the size of the image ___________________
When the object is placed at C, the image appears at ___________ and it is the ________________ size.
As the object moves inside C, approaching F, the image forms ______________ away and the size of the image is _______________ than the actual object. At F, _______ image forms since the reflected rays are ___________________
When the object is between F and V, the reflected rays ____________________. Since our eye believes that light travels in a straight line, our brain takes these diverging rays back to the place where we think they meet, behind the __________________. We say this image is ______________ because the rays don't really go behind the mirror. * Remember that all rays drawn behind the mirror should be dotted because light does not really travel behind the mirror.
http://boomeria.org/physicstextbook/ch13.html
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The Magnification Equation and the Mirror Equation
Scientists often collect data to look for patterns in the result. By completing the following table, definite relationships will emerge.
do
ho
hi
object
di
Measurements from Ray Diagrams for a Concave Mirror
ho
do
hi
di
f
(cm)
(cm)
(cm)
(cm)
(cm)
di
___
do
hi
___
ho
1
1
___
___
+
di
do
(cm­1)
1
___
f (cm­1)
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Derived Equations
physics site with more mirror euations
From this analysis, two unique equations emerge. The Magnification Equation
_ ___
hi
di
___
M = =
ho
do
The Mirror Equation
1
1
1
___
___
___
=
+
di
do
f Sign convention.
To deal with the different types of images, the following sign convention is used.
• inverted images have a negative height
• virtual images have a negative distance to the image
• diverging mirrors (Convex mirrors) have a negative focal length.
Use the two equations to answer the following word problems.
1. A concave mirror has a focal length of 6.0 cm. An object with a height of 0.60 cm is placed 10.0 cm in front of the mirror.
a) Calculate the image distance.
b) Calculate the image height.
2. A concave mirror has a focal length of 2.0 cm. An object with a height of 1.0 cm is placed 1.0 cm in front of the mirror.
a) Calculate the image distance.
b) Calculate the image height.
3. A concave mirror has a focal length of 3.0 cm. An object with a height of 3.0 cm is placed 8.0 cm in front of the mirror.
a) Calculate the image distance.
b) Calculate the image height.
4. A member of "Pippin" is applying make­up using a concave mirror. The actor's face is 35 cm in front of the mirror and the image is 72 cm behind the mirror (virtual).
a) What is the magnification of the mirror?
b) Use the mirror equation to determine the focal length of the mirror. (do not forget about the sign convention.
5. A concave mirror magnifies an object placed 30.0 cm from the mirror by a factor of +
3.0 . Calculate the radius of curvature of the mirror. Assume that the image is a real image.
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Mr. P's variation on GRASP 1. Read the question carefully and sketch the information in a picture.
2. Carefully record all measures with their appropriate units in the sketch.
3. Write the appropriate formula(s) below the sketch and place all the variables in the margin. You must think carefully at this time ­ it is the most important step. The units on each measure can help guide you in the selection of the proper formulas but your knowledge on the theory involved plays a greater role. (this applies more to grade 11 and 12 physics ­ for these problems, there are only 2 possible formulas)
4. Transfer all the information from the sketch to the measures indicated in the margin, with units.
5. Look for any hidden information or necessary steps that are implied in question
• unit conversions
• sign conventions (certain values negative)
6. Plug the known variables into the equation and solve mathematically. Do not stress over math. In science, math is a tool just like language is a tool to communicate information. The selection of the proper equation, the identifying of the correct measures, the correct application of the units with any conversions, the application of the correct sign equation, the recording of an answer with the correct unit are equally as important as performing the math correctly. (5 out of 6 steps are not based on math)
7. Report your answer accordingly ensuring units present.
Example Determine the location of the image and the height of the image of a 3.0 cm object placed 8.0 cm from a concave mirror with a focal length of 5.0 cm.
M = di =
_ ___
hi
di
___
=
ho
do
1
1
1
___
___
= ___
+
di
do
f do =
hi =
ho =
f =
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