Physics 222 Spring 2009 Exam 3 Version C (852429)
Question
1 2 3 4 5 6 7 8 9 10
Instructions
Be sure to answer every question. Follow the rules shown on the first page for filling in the Scantron form. Each problem is worth 10%
of the exam. When you are finished, check with Dr. Mike or his TA to be sure you have finished the scantron correctly.
1.
Question Details Mirror Equations and Magnification (3) [750390]
Dr. Mike stands in front of a CONVEX mirror. He looks at the image of his eye. It is UPRIGHT and half the size of his real eye. If f is the
focal point of the mirror, how far is he standing from the front of the mirror?
y*04*f/2
z*04*2f
x*03*3f/8
v*10*f
w*03*2f/3
Solution or Explanation
For this situation, the linear magnification is +1/2. Thus, we have
+1/2 = - di / do
or
di = - do / 2.
Using this in the mirror equation, we find
f = [1 / do - 2 / do]-1 = - do.
Therefore,
do = - f.
2.
Question Details Mirror Equation (4) [750392]
Plane mirrors and convex mirrors form virtual images. With a plane mirror, the image may be infinitely far behind the mirror, depending on
where the object is located in front of the mirror. For an object in front of a single convex mirror, what is the greatest distance behind the
mirror at which the image can be found? Assume that R is the radius of the mirror
y*03*3R/4
v*10*R/2
x*05*2R
w*05*R
z*03*4R/3
Solution or Explanation
Look at the mirror equation, and solve for the image distance.
di = (1/f - 1/do)-1.
If f is a negative number (as it is for a convex mirror) and do is positive (as it always is for a single mirror or lens), then the largest
possible distance of the image behind the mirror is when the object is infinitely far away. Thus, the image is at
di = -f = -R/2,
which is R/2 behind the mirror.
3.
Question Details Mirror Equation or Ray Trace (3) [750394]
A concave mirror (R = 64 cm) is used to project a transparent slide onto a wall. The slide is located at a distance of 40.0 cm from the
mirror, and a small flashlight shines light through the slide and onto the mirror. The setup is similar to that in Figure 25.19a.
Figure 25.19a.
The height of the object on the slide is 1.70 cm. What is the height of the image? (Make sure you give the proper sign in this case!)
y*04*-0.43 cm
v*10*-6.80 cm
z*02*0.43 cm
x*03*4.53 cm
w*05*6.80 cm
Solution or Explanation
Since the mirror is concave and spherical, it has a focal length of +R/2 = +32.0 cm. Also, since the image is in front of the mirror, it is
positive as well. 40.0 cm is the object distance since the slide is the object and it is positive too.
The image is the projection on the wall, so the distance to the wall from the mirror must be the image distance. Thus, we can use the
mirror equation to find
di = (1/f - 1/do)-1 = 160.00 cm.
The height of the object on the slide is ho and may be positive or negative depending on whether the object is considered to be right side
up or upside down. Normally, we assume the object to be positive in height regardless of its actual orientation. This is why we use a
positive number here for the object height. Using the linear magnification equation, we have
hi = - ho di / do = -6.80 cm.
Note that this is negative because it is inverted and the object height is positive.
4.
Question Details Ray Trace or Thin-Lens Equation (1) [1093275]
Do a ray trace for the object and mirror shown here or use the number of blocks to do the thin-lens equation. Determine which of the
following describes the image.
v*10*It is virtual, upright, and smaller than the object.
y*02*It is real, upright, and larger than the object.
z*02*It is virtual, inverted and larger than the object.
w*04*It is real, inverted, and smaller than the object.
x*04*It is virtual, upright, and larger than the object.
Solution or Explanation
5.
Question Details Apparent Depth (1) [750391]
A silver medallion is actually 1.73 cm beneath the surface of a calm pool. How far below the surface of the pool would someone see the
medallion if they were viewing it from above the pool? (In other words, what is its apparent depth?)
Note: The refractive index of water is 1.33.
x*04*0.77 cm
v*10*1.30 cm
w*01*2.30 cm
z*00*1.73 cm
y*03*0.58 cm
Solution or Explanation
The apparent depth is
d' = d (1) / nwater = 1.30 cm.
6.
Question Details Reflection and Mirrors (1) [750389]
Bailey-the-Wonderdog sees a reflection of herself in a mirror. When she does so she notices that the dog she sees in the image is
smaller than she is. What is the shape of the mirror?
w*05*Concave
x*01*Flat
y*05*Convex
v*10*Convex or Concave would both give this result.
z*01*There is no mirror that would give this result.
Solution or Explanation
There are cases where this is true for both types of mirror. For instance, if we combine the mirror equation with the magnification
equation, we get
m = 1 / (do / f -1).
Then, when f = 1 and do = 3, we have m = -1/2. Also, when f = -3 and and do = 3, we get m = 1/2. In both cases, the absolute value of
the magnification is less than 1 and the image is smaller.
There really is no way to tell without drawing the ray trace or doing the equations.
Although both mirrors can give smaller images, the two types of mirrors do NOT both give larger images. Only one does this. Can you
figure out which one?
7.
Question Details Ray Trace or Thin-Lens Equation (1) [1092933]
Do a ray trace for the object and mirror shown here or use the number of blocks to do the thin-lens equation. Determine which of the
following describes the image.
z*02*It is virtual, inverted and smaller than the object.
w*04*It is real, inverted, and larger than the object.
x*04*It is virtual, upright, and smaller than the object.
y*02*It is real, upright, and smaller than the object.
v*10*It is virtual, upright, and larger than the object.
Solution or Explanation
The ray trace is shown below.
8.
Question Details What can we see? (3) [750393]
A person 1.58 m tall wants to be able to see her full image in a plane mirror. How far above the floor should the bottom of the mirror be
placed so that she can see her feet, assuming that the top of the person's head is 20 cm above her eye level?
z*01*0.2 m
w*05*0.99 m
x*03*1.48 m
v*10*0.69 m
y*06*0.79 m
Solution or Explanation
This problem is easy if you draw a diagram!
The minimum height for the mirror must allow for light from her feet and the top of her head to reach her eyes. A ray diagram will easily
show this to be 1/2 her height.
If the top of her head is 20 cm above her eyes, then the light from her head as it goes to her eyes must hit the mirror 10 cm below her
head (the position of the top of her head is her height.) Thus, the top of the mirror is 10 cm less than her height (1.48 m) and the bottom
is half her height below that (0.790 m), or 0.690 m.
9.
Question Details Ray Trace or Mirror Equation (1) [1092934]
Do a ray trace for the object and mirror shown here or use the number of blocks to do the mirror equation. Determine which of the
following describes the image.
z*02*It is virtual, inverted and smaller than the object.
x*04*It is virtual, upright, and smaller than the object.
y*02*It is real, upright, and smaller than the object.
w*04*It is real, inverted, and larger than the object.
v*10*It is virtual, upright, and larger than the object.
Solution or Explanation
The ray trace is shown below.
10.
Question Details Total Internal Reflection (2) [749486]
A ray of light falls on a rectangular glass block (n = 1.47) that is almost completely submerged in water (n = 1.33) as shown in Figure 3359.
Figure 33-59
In this case, we can find an angle for which total internal reflection occurs at the point P. Would total internal reflection occur at point P
for this same value of if the water were replaced by another fluid with index of refraction n = 1.41?
v*10*No
w*04*Yes
x*03*It depends on the value of .
y*03*It depends on the frequency of the light.
z*01*There is no way to determine the answer.
Solution or Explanation
The angle necessary to get total internal reflection is given by the equation
-1
c = sin (n2 / n1).
Any angle less than this will also refract. For the case with water we have n2 = 1.33 and for the other fluid n2 = 1.41. The value of n1 =
1.44 in both cases.
As you can see by chacking the equations, c is greater for the other fluid than it is for water. If was just big enough for the angle at P
to be c when the water is present, then the same gives us the same angle at P even with the fluid present. Thus, the new angle is
less than the c for the fluid and refraction will occur.
Assignment Details
Name (AID): Physics 222 Spring 2009 Exam 3 Version C (852429)
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