Download Concave Mirrors

Buggé: Optics 4
Concave Mirrors
4.1 Recall, how does light reflect off of a plane mirror? Draw a ray diagram.
4.2 Observe and Explain Observe the video of the parallel light beams reflected off of the concave mirror.
Explain why the light beams are reflected this way using the law of reflection. Draw a diagram that represents
what happens when beams of parallel light strike the concave mirror. The special point that they all converge to
is called for the focal point of the mirror.
4.3 Four Special Rays
There are four rays that are easy to draw for concave mirrors. Draw each below:
1) An incident ray that is parallel to the optical axis:
2) An incident ray that travels through the focal point of the mirror:
3) An incident ray that strikes the mirror at the optical axis:
4) An incident ray that strikes the center of the mirror:
Buggé: Optics 4
4.4 Try it yourself
Spongebob Squarepants stands 3 meters in front of a concave mirror that has a focal point 1 meter from the
surface of the mirror.
a) Draw a ray diagram for the situation:
b) What will Spongebob’s image look like – will it be… (magnified or reduced?) (real or virtual?) (upright or
inverted?)
4.5 Try it yourself
Spongebob now stands 0.5 meters in front of a concave mirror that has a focal point 1 meter away from the
surface of the mirror.
a) Draw a ray diagram for the situation
b) What will Spongebob’s image look like – will it be… (magnified or reduced?) (real or virtual?) (upright or
inverted?)
Buggé: Optics 4
4.6 Design an Experiment
Design an experiment to experimentally locate the focal length of a mirror. Write or draw your set up below.
4.7 Derive The ray diagram and the reasoning that follows allows you to derive a mathematical relationship between the distance of
the object from a mirror do, the distance of the image from the mirror di, and the focal length of the mirror f. Carefully examine the
derivation and evaluate the outcome using limiting case analysis and your knowledge of how lenses form images of objects. AB is a
bright object; A1B1 is the image of the object. (M, N, and C are points on the mirror, where rays hit it.)
A
M
B1
F
C
N
O
B
A1
f
do
•
•
•
•
•
di
AM ≈ BC = do (the rays are close to the main axis of the mirror).
A1N ≈ B1C = di; CM ≈ BA, and CN ≈ B1 A1.
ABF and CNF are similar triangles. Thus BF/CF = AB/A1B1 or (do-f)/f = AB/ A1B1.
A1B1F and MCF are similar triangles. Thus CF/B1F = CM/A1B1 = AB/A1B1 = f /(di– f).
From this, we find
do − f
f
=
f
di − f
or, after some algebra, we get a relationship that is called the mirror equation:
€
1 1 1
+ = .
do d i f
(a) Does the relationship make sense when the object is infinitely far away? Support your answer with a ray diagram.
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(b) Does the relationship make sense if an object is placed right at the focal point? Support your answer with a ray diagram.
(c) Does the relationship make sense when the object is between the mirror and the focal point? Support your answer with a ray
diagram.
(d) Describe carefully all the assumptions that we made deriving the relationship.
Buggé: Optics 4
Homework
4.8 Regular problem Use ray diagrams and the mirror equation derived in class to locate the position,
orientation, and type of image formed by an upright object held in front of a concave mirror of focal length +20
cm. The object distances are (a) 200 cm, (b) 40 cm, and (c) 10 cm.
4.9 Regular problem A large concave mirror of focal length +3.0 m stands 20 m in front of you. Describe the
changing appearance of your image as you move from 20 m to 1 m from the mirror. Indicate distances from the
mirror where the change in appearance is dramatic.
4.10 Regular Problem
Location the position, orientation, and type of image formed by an upright object held in front of a concave
mirror of focal length + 50 cm. The object distance is 100 cm. Include a ray diagram.
4.11 Regular Problem
Locate the position, orientation, and type of image formed by an upright object held in front of a concave mirror
of focal length +50 cm. The object distance is +25 cm. Include a ray diagram.
4.12 Regular Problem
Locate the position, orientation, and type of image formed by an upright object held in front of a concave mirror
of focal length + 3m. The object distance is 2.5m. Include a ray diagram.
4.13 Regular Problem
Locate the position, orientation, and type of image formed by an upright object held in front of a concave mirror
of focal length +26 cm. The object distance is 32cm.