Light, Reflection and Mirrors
© The Physics Classroom, 2009 Page 1
Name: __________________________________________________________
Light Reflection
Read from Lesson 1 of the Reflection chapter at The Physics Classroom: http://www.physicsclassroom.com/Class/refln/u13l1a.html /
http://www.physicsclassroom.com/Class/refln/u13l1b.html / http://www.physicsclassroom.com/Class/refln/u13l1c.html
1. Place a letter in the blank in order to classify the following objects as being either luminous (L) or illuminated (I) objects.
Sun _____ Moon _____ Person _____ Whiteboard _____ Light bulb _____ Candle _____
2. These diagrams are intended to represent the path of light from an object to an eye as the eyesights at the image of the object. Each
diagram is incorrect. Discuss what makes them incorrect.
Discussion:
3. State the law of reflection in the space below.
Discussion
Consider the diagram at the right in answering the next three questions.
4. The angle of incidence is denoted by angle ____.
5. The angle of reflection is denoted by angle ____.
6. If an incident ray of light makes an angle of 35° with the mirror surface then the angle of reflection is _______°.
7. Why do windows of distant houses appear to reflect the sun only when rising or setting? Explain in words. Use the
diagram to help, drawing appropriate light rays on the diagram.
8. Use the law of reflection and the embedded protractor in order to draw the reflected ray associated with the given incident ray for the
following plane mirror situations. (Markings are provided at 15° increments.)
9. Now for a research question:
In this unit we will often discuss how the reflection of light from a mirror results in the formation of an image. The term image as used
here has an obvious context - physics. But the term image has numerous other contexts - psychology (a positive self-image), religion
(created in God's image), business (the company's image), medicine (an x-ray image), etc. Your research question involves finding a
dictionary and looking up the definition of the word image. Write down several meaningful definitions from several contexts in the spaces
below. (If you do not have a dictionary at home then you can use dictionary.com or wikipedia.org.)
a.
b.
c.
d.
e.
10. Now write in your own words a personal definition of what you believe an image of an object is:
Specular (Regular) versus Diffuse Reflection
Read from Lesson 1 of the Reflection chapter at The Physics Classroom: http://www.physicsclassroom.com/Class/refln/u13l1d.html
1. Describe the difference between diffuse reflection and regular (or specular) reflection.
2. Explain what causes light rays to undergo diffuse reflection.
3. Which one of the following diagrams depicts diffuse reflection? ________
4. True or False: When a beam of light undergoes diffuse reflection, individual rays within the beam do NOT follow the law of reflection.
Explain your answer.
5. For each of the five surfaces given below, draw normal lines.
6. Consider the diagram at the right of five rays of light approaching a microscopically
rough surface. For each incident ray, estimate the normal line and draw the
corresponding reflected ray of light.
7. Identify whether the following phenomenon are attributable to diffuse reflection (DR) or regular reflection (RR):
a. The image of a mountain can be clearly seen in the calm waters of a lake. _______
b. A lacquered tabletop produces a glare of the lamp bulb in the overhead light. _______
c. Water is sprayed onto a sheet of paper. A laser beam is directed towards the paper, reflects and produces a red dot on the ceiling. _______
d. Light from the overhead lights strikes your body and reflects towards all your classmate's eyes. _______
8. A microscopic view of a sheet of paper is shown in the diagram at the right. Would you expect this sheet of
paper to cause light to undergo regular or diffuse reflection? ____________ Explain.
A microscopic view
of a sheet of paper.
9. From what type of surface do you think it would be easier to read? From pages that are rough or
from pages which are smooth and glossy? _________________________. Explain your answer.
10. Driving at night offers a great example of diffuse vs. regular
reflection. A dry road is a diffuse reflector, while a wet road is
not. On the diagrams to the right, sketch the reflected light off a
wet and dry surface.
Why would the wet road appear to the driver to be darker than the
dry road?
11. The diagram below contrasts the reflection of light off a smooth surface (left) with the reflection of light off a rough surface (right).
Compare the two diagrams and explain why the reflected rays for a rough surface do not result in the formation of an image.
Image Formation and Characteristics
Read from Lesson 2 of the Reflection chapter at The Physics Classroom: http://www.physicsclassroom.com/Class/refln/u13l2a.html ,
http://www.physicsclassroom.com/Class/refln/u13l2b.html , & http://www.physicsclassroom.com/Class/refln/u13l2c.html
1. An object (denoted by a dark circle) is placed in front of a plane mirror as shown below. Light from the object emanates in a variety of
directions. For each light ray incident to the mirror, accurately draw the corresponding reflected ray. Use a protractor, straight-edge, and
the law of reflection.
2. For each reflected ray drawn in the diagram above, use dashed lines to trace the reflected ray backwards behind the mirror. If done
correctly, all reflected rays should intersect at the same location; this location corresponds to the image location.
3. Make measurements on the diagram to compare the object distance (distance from the object to the mirror) to the image distance (distance
from the intersection point or image location to the mirror). Record the results of your comparison in the space below.
4. The image of an object as formed by a plane mirror is located ____.
a. on the mirror surface b. in front of the mirror surface c. behind the mirror surface d. any of the above, depending on the object's location.
5. Which of the following statements are true of plane mirror images? List all that apply in alphabetical order with no spaces between letters.
a. The location of an image is different for different observers.
b. Observers at different locations will sight along different lines at the same image.
c. Every image is located on the mirror surface and at the same location for different observers.
d. Every image is located on the mirror surface, but at a different location for different observers.
e. All observers (regardless of their location) will sight at the same image location.
6. The diagram below depicts the path of four incident rays emerging from an object and approaching a mirror. Five lettered locations are
shown on the opposite side of the mirror. Which location is representative of the image location?
7. The diagram below depicts the path of four reflected rays that originated at the object on the left side of the mirror and have subsequently
reflected from the mirror. Five lettered locations are shown on the right side of the mirror. Which location is representative of the image
location?
Ray Diagrams
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Four Steps to Drawing Ray Diagrams
Plane mirror ray diagrams show how light travels from an object to the mirror to an eye in order for the eye to view the image of the object.
There are four steps to the construction of a ray diagram.
i. Draw the image of the object.
ii. Pick one extreme on the image of the object and draw the reflected ray that will travel to the eye as the eyesights at this point.
iii. Draw the incident ray for light traveling from the corresponding extreme on the object to the mirror.
iv. Repeat steps ii and iii for all other extremities on the object.
Locating Images
1. Locate all of the images for the following objects (labeled "o") as produced by the mirror (labeled "m"). Consider steps 1 and 2 above.
Drawing Ray Diagrams
Questions #2 - #11 provide a detailed procedure for the completion of a ray diagram. The diagram at the right shows an arrow (the object), a
plane mirror, and an eye. Use this diagram and a ruler/straight edge to do the following steps.
2. Locate the image of points A and B.
Label these points as A' and B'.
3. Draw in the complete image.
Compare the size of the image to the size of the object.
4. If the eye is to see A by looking in the mirror,
then the eye must sight along a line at the image of A (i.e., A').
Draw the reflected ray which reaches the eye as it sights at A'.
Use a solid line and an arrowhead.
5. Extend this reflected ray beyond the mirror using a dashed line
to show that the eye is sighting along a line directly at A'.
6. The light that follows the path shown by the reflected ray originated from point A. Show this by accurately drawing the incident ray that
starts at point A and approaches the mirror. Be sure to use a solid line and put an arrow upon the ray.
7. Repeat steps #4-#6 in order to show how light travels from point B to the mirror and reflects towards the eye as the eye sights along a line
at B'.
8. On the diagram, label the point on the mirror where the incident ray from A reflects from the mirror with the letter "x".
9. On the diagram, label the point on the mirror where the incident ray from B reflects from the mirror with the letter "y".
10. Points "x" and "y" represent the points on the mirror which would be needed to view point A and point B on the object. Where will any
other ray from the object reflect from the mirror before traveling to the eye?
11. What parts of the mirror could be removed without interfering with the eye's ability to see the entire image of the arrow? Circle these
sections of the mirror.
12. For the following objects, (a) draw the corresponding images, and (b) draw and label the incident and reflected rays which would allow
the eye to view the object in the mirror (labeled "m").
13. Front row students Al, Bo, Cy, Di, Ed and Fred are looking into a 4-foot long mirror that
the teacher strategically placed on the demonstration table. Their positions are shown in
the diagram below. In the diagram, locate their images and complete the given statements.
Al can see...
Di can see...
Bo can see...
Ed can see...
Cy can see...
Fred can see...
14. The teacher asked the six students to assume different positions in the room. Their positions are shown below. Determine and label the
image locations and complete the given statements.
Al can see...
Di can see...
Bo can see...
Ed can see...
Cy can see...
Fred can see...
15. Consider the mirror and the stick-person shown in the two diagrams below. The distance between the mirror and the person is different in
the two diagrams. For each diagram, accurately draw and label the image of the stick-person in the appropriate position. Finally, draw
lines of sight from the eyes of the stick-person to the mirror in order to indicate which portion of the mirror is needed to view the image.
Use a ruler/straight-edge and be precise.
16. Compare the height of the stick-person to the length of mirror needed to view the stick-person. Make some measurements (from the
diagram above) and record below.
17. Does the distance from the stick-person to the mirror seem to effect the amount of mirror that the person needs to view the image?
________ Explain and support your answer using numerical values taken from question #15 above.
Curved Mirrors and The Law of Reflection
Read from Lesson 3 of the Reflection chapter at The Physics Classroom: http://www.physicsclassroom.com/Class/refln/u13l3a.html
The diagram below depicts a concave mirror with its principal axis and its center of curvature (C). Five incident rays are shown traveling
parallel to the principal axis.
1. Construct normal lines for each of the five incident rays. (Geometry Review: A line that passes through the center of a circle will be
perpendicular to the circle at its point of intersection. Thus, the normal line for each of these incident rays passes through C.)
2. Measure the angle of incidence and use the law of reflection to construct five reflected rays at the appropriate angle of reflection.
3. Construct two more incident rays parallel to the principal axis that strike points 6 and 7. Draw the normal line and use the law of reflection
to draw the corresponding reflected rays.
4. Label the focal point (F) on the diagram above.
5. Propose your personal definition of the focal point: The focal point is ...
6. Make some generalized statements about rays 1-5 and about rays 6-7. How are they similar and how are they different?
The diagram below depicts a convex mirror with its principal axis and its center of curvature (C). Five incident rays moving parallel to the
principal axis are shown.
7. As on the front side, construct normal lines for each of the five incident rays. (Geometry Review: A line that passes through the center of a
circle will be perpendicular to the circle at its point of intersection. Thus, the normal line for each of these incident rays passes through C.)
8. Measure the angle of incidence and use the law of reflection to construct five reflected rays at the appropriate angle of reflection.
9. For each reflected ray, construct extensions of the rays backwards behind the mirror until they
intersect the principal axis.
10. Make some generalized statements about rays 1-5 to describe how they reflect.
Conclusion: Propose a rule of reflection for both concave and convex mirrors which would describe how incident rays parallel to the
principal axis would behave upon reflection.
Spherical Mirrors
Read from Lesson 3 of the Reflection chapter at The Physics Classroom: http://www.physicsclassroom.com/Class/refln/u13l3a.html / ,
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1. A spherical mirror has a shape which is a section of a sphere. Consider the concave
spherical mirror shown at the right. Label the following on the diagram:
• the principal axis (a line) as PA
• the focal point (a point) as F
• the center of curvature (a point) as C
• the focal length (a length) as f
• the radius of curvature (a length) as R
2. Explain why concave mirrors are sometimes called converging mirrors.
3. Explain why convex mirrors are sometimes called diverging mirrors.
4. The diagrams below show three incident rays. For each diagram, draw the three corresponding reflected rays on the diagrams. Place
arrowheads upon all your rays. (Study the ray diagrams in your textbook carefully to answer these questions.)
5. State the three rules which describe the predictable reflection of three rays of incident light for a concave mirror. (See question #4.)
6. Light from a distant star is collected by a concave mirror. How far from the mirror do the light rays converge if the radius of curvature of
the mirror is 150 cm?
7. Suppose your teacher gives you a concave mirror and asks you to find the focal point. Describe the procedure you would use to do this.
8. The image location is the location in space from where it would seem to every
observer as though reflected light is coming from. The diagram at the right shows an
object and a concave mirror. Four rays of light from the object approach the mirror.
Note that ray 1 and ray 4 are two of the three principal rays whose behavior are
described in question #5 above. Reflect each ray (starting with rays 1 and 4) and
determine the image location. Put a dot at the image location and label it image.
9. Consider the diagram at the right of an object, an image, and a concave mirror. On
the diagram, show the path of light from object to the mirror to the eye as the eye
sights at the image.
Ray Diagrams for Concave Mirrors
Read from Lesson 3 of the Reflection chapter at The Physics Classroom: http://www.physicsclassroom.com/Class/refln/u13l3d.html &
http://www.physicsclassroom.com/Class/refln/u13l3e.html
For the following mirrors and corresponding object positions, construct ray diagrams. Then describe the Location of the image, Orientation
(upright or inverted) of the image, the relative Size of the image (larger or smaller than object), and the Type of image (real or virtual).
For Case 4, merely construct the ray diagram.
NOTE: 1) All light rays have arrowheads which indicate the direction of travel of the ray.
2) Always draw in the image once located (an arrow is a good representation).
3) Exactness counts. Use a straight-edge and be accurate.
Case 1: If the object is located "beyond" the center of curvature.
Description of Image: _________________________________________ Location: _________________________________________
O: Upright or Inverted
S: Magnified or Reduced
T: Real or Virtual
Case 2: If the object is located at the center of curvature.
Description of Image: _________________________________________ Location: _________________________________________
O: Upright or Inverted
S: Magnified or Reduced
T: Real or Virtual
Case 3: If the object is located between the center of curvature and the focal point.
Description of Image: _________________________________________ Location: _________________________________________
O: Upright or Inverted
S: Magnified or Reduced
T: Real or Virtual
Case 4: If the object is located at the focal point.
No Description Required
Case 5: If the object is located between the focal point and the mirror.
Description of Image: _________________________________________ Location: _________________________________________
O: Upright or Inverted
S: Magnified or Reduced
T: Real or Virtual
Ray Diagrams for Convex Mirrors
Read from Lesson 4 of the Reflection chapter at The Physics Classroom: http://www.physicsclassroom.com/Class/refln/u13l4b.html &
http://www.physicsclassroom.com/Class/refln/u13l4c.html
For the following mirrors and corresponding object positions, construct ray diagrams. Then practice the LOST art of image description.
Identify the Location of the image, Orientation (upright or inverted) of the image, the relative Size of the image (larger or smaller than
object), and the Type of image (real or virtual).
NOTE: 1) All light rays have arrowheads that indicate the direction of travel of the ray.
2) Always draw in the image once located (an arrow is a good representation).
3) Exactness counts. Use a straightedge and be accurate.
Case 1: Object is Relatively Close to Mirror
Description of Image: _________________________________________ Location: _________________________________________
O: Upright or Inverted
S: Magnified or Reduced
T: Real or Virtual
Case 2: Object is Relatively Far Away from Mirror
Description of Image: _________________________________________ Location: _________________________________________
O: Upright or Inverted
S: Magnified or Reduced
T: Real or Virtual
Mathematics of Curved Mirrors
Read from Lessons 3 and 4 of the Reflection chapter at The Physics Classroom: http://www.physicsclassroom.com/Class/refln/u13l3f.html &
http://www.physicsclassroom.com/Class/refln/u13l4d.html
Use the mirror equation and the magnification ratio to solve the following problems. PSYW
1. Bobby places a 4.25-cm tall light bulb a distance of 36.2 cm from a concave mirror. If the mirror has a focal length of 19.2 cm, then what
is the image height and image distance?
2. Van Itee, quite concerned about the pimple on his chin, is looking into a concave mirror with a focal length of 33.6 cm. Determine the
image height and image distance of the 2.50-mm sized pimple when placed 25.2 cm from the mirror.
3. Al Wayscurious is intrigued by the reflective abilities of his family's soup ladle. The ladle acts as a concave mirror with a 2.59-cm focal
length. Determine the image size of a Al's 24.8-cm tall face when placed 12.8 cm from the ladle's surface.
4. Mr. H splurged when he bought his Yugo and ordered the side mirror option. The mirror has a focal length of -88.4 cm. What is the image
height of a 4.59-meter tall truck when located 12.6 meters away from the mirror?
5. A Christmas tree ornament with a 8.64-cm diameter serves as a convex mirror surface. Determine the image size and the image distance of
a 4-foot tall child standing a distance of 2.65 meters away.
Object-Image Relations
Read from Lesson 3 of the Reflection chapter at The Physics Classroom: http://www.physicsclassroom.com/Class/refln/u13l3d.html &
http://www.physicsclassroom.com/Class/refln/u13l3e.html
1. A 10.0-cm tall object is placed in front of a concave mirror with a focal length of 20.0 cm. For each object distance, calculate the image
distance, magnification, and image height. Sketch a ray diagram showing the object in the appropriate location and the image with the
proper location, orientation and relative size.
do
di
Mag
hi
Ray Diagram Sketch
A
50 cm
B
40 cm
C
30 cm
D
20 cm
e
10 cm
2. Arrows numbered 1-8 represent object locations for a concave mirror. For each of these objects, use your understanding of image
characteristics to determine the corresponding image location, orientation and relative size. Since these diagrams have not been created to
scale, do NOT use ray diagrams to determine your answers.
Object
1
2
3
4
Image
Object
5
6
7
8
Image
3. Arrows numbered 1-4 represent object locations for a convex mirror. For each of these objects, use your understanding of image
characteristics to determine the corresponding image location, orientation and relative size. Since these diagrams have not been created to
scale, do NOT use ray diagrams to determine your answers.
Object
1
2
Image
Object
3
4
Image
Light Refraction
Read from Lesson 1 of the Refraction and Lenses chapter at The Physics Classroom: http://www.physicsclassroom.com/Class/refrn/u14l1a.html ,
http://www.physicsclassroom.com/Class/refrn/u14l1b.html , http://www.physicsclassroom.com/Class/refrn/u14l1c.html &
http://www.physicsclassroom.com/Class/refrn/u14l1f.html
1. Write a one-word synonym for refraction.
2. Refraction occurs when light crosses the boundary between one material and another material. What is the primary cause for this refracting
of light upon crossing a boundary?
The diagram below shows the path of a light ray as it travels through air, across the air-water boundary, and through the water. Use the
diagram to answer questions #3-#6.
3. On the diagram, label ...
• the air-water boundary with a B
• the normal line with an N
• the incident ray with an I
• the refracted ray with an R
• the angle of incidence with a θi
• the angle of refraction with a θr
4. How many media are there in this diagram? _____
Name them.
5. What is meant by the term "medium" in this context?
6. Place a noticeable dot at the location where refraction of light takes place.
7. For the three situations below, draw a normal line and measure and record the angles of incidence and the angles of refraction.
8. As light passes from one medium into another, it refracts. There is only one condition in which light will cross a boundary but not refract.
State this condition.
Direction of Bending
Read from Lesson 1 of the Refraction and Lenses chapter at The Physics Classroom: http://www.physicsclassroom.com/Class/refrn/u14l1d.html ,
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1. The optical density is the property of a medium which provides a relative measure of the speed at which light travels in that medium. Light
travels __________________ (fastest, slowest) in media with a greater optical density.
2. Every transparent material is characterized by a unique index of refraction value (n). The index of refraction value is a numerical value
which provides a relative measure of the speed of light in that particular material. Light travels __________________ (fastest, slowest) in
media with a higher index of refraction value.
3. The speed of light (v) in a material is determined using the speed of light in a vacuum (c) and the
index of refraction (n) of the material. Calculate the speed of light in the following materials.
a. water (n = 1.33): __________________
b. glass (n = 1.50): __________________
c. ice (n = 1.31): __________________
d. diamond (n = 2.42): __________________
4. When light passes into a medium in which it travels faster, the light will refract ________ the normal.
When light passes into a medium in which it travels slower, light will refract ________ the normal.
a. towards, away from b. away from, towards
5. When light passes into a medium that is more optically dense, the light will refract ________ the normal. When light passes into a medium
that is less optically dense, the light will refract ________ the normal.
a. towards, away from b. away from, towards
6. Consider the refraction of light in the five diagrams below. In which case is the light bending towards the normal line? Circle all that apply.
Consider the diagram at the right in answering the next four questions.
7. There are ___ (1, 2, 3, ...) media shown in the diagram.
8. There are ___ (1, 2, 3, ...) boundaries shown in the diagram.
9. Light must travel __________ in medium 1 compared to medium 2.
a. slower
b. faster
c. insufficient info
10. Light must travel __________ in medium 2 compared to medium 3.
a. slower
b. faster
c. insufficient info
11. In each diagram, draw the "missing" ray (either incident or refracted) in order to appropriately show that the direction of bending is
towards or away from the normal.
12. A ray of light is shown passing through three consecutive layered materials. Observe the direction of bending at
each boundary and rank the three materials (A, B and C) in order of increasing index of refraction.
________________ ____
< ____________________ < ____________________
smallest
largest
13. Arthur Podd's method of fishing involves spearing the fish while standing on the shore. The
apparent location of a fish is shown in the diagram below. Because of the refraction of light,
the observed location of the fish is different than its actual location. If Arthur is to
successfully spear the fish, must he aim at, below, or above where the fish appears to be?
__________ Explain.
Snell's Law Read from Lesson 2 of the Refraction and Lenses chapter at The Physics Classroom:
http://www.physicsclassroom.com/Class/refrn/u14l2b.html
http://www.physicsclassroom.com/Class/refrn/u14l2c.html
http://www.physicsclassroom.com/Class/refrn/u14l2d.html
Math Review:
To find an angle measure for which the sine value is 0.8660, enter 2nd Sin (0.8660) into your TI graphing calculator and press the Enter key.
The angle is 59.99... degrees.
1. Use Snell's law to solve the following physics word problems. PSYW
a. An incident ray in air (n=1.0) is approaching the boundary with an unknown material at an angle of incidence of 61.6°. The angle of
refraction is 41.4°. Determine the index of refraction of the unknown material.
b. An incident ray in air (n=1.0) is approaching the boundary with glass (n = 1.52) at an angle of incidence
of 32.5°. Calculate the angle of refraction. Draw the refracted ray on the diagram at the right.
2. For the following two situations, measure and record θi, calculate θr, and draw in the refracted ray with the calculated angle of refraction.
PSYW Light, Refraction and Lenses
3. The diagram at the right shows a light ray entering a rectangular block of unknown material and
subsequently exiting the block on the opposite side. The path of the light ray through the block
is shown. Determine the index of refraction of the unknown material. Perform two calculations
– one for each boundary - using Snell's law and the measured angles. PSYW
4. Cal Culator is performing experiments to determine the index of refraction of two unknown materials. Cal determines that the light follows
the paths as shown on the diagrams below. Use this path, a protractor, a calculator and Snell's Law to determine the index of refraction of
the unknown material. Show all your work in the space beside the diagram.
Total Internal Reflection Read from Lesson 3 of the Refraction and Lenses chapter at The Physics Classroom:
http://www.physicsclassroom.com/Class/refrn/u14l3a.html
http://www.physicsclassroom.com/Class/refrn/u14l3bhtml
http://www.physicsclassroom.com/Class/refrn/u14l3c.html
Background:
Whenever a light ray reaches the boundary with a transparent medium, a portion of the light energy is transmitted across the boundary and
appears as a refracted ray; and a portion of the energy remains within the original medium and appears as a reflected ray. The path of the
refracted ray follows Snell's law. The path of the reflected ray follows the law of reflection. The amount of light energy that is reflected
and transmitted is dependent upon the angle of incidence. At certain angles, all of the light is reflected (none is transmitted) and remains
inside the original medium. This is known as total internal reflection (TIR).
1. Light will undergo total internal reflection only when it is _______. Choose two.
a. in the less dense medium traveling towards the more dense medium
b. in the more dense medium traveling towards the less dense medium
c. in the medium where it travels slowest, moving towards the medium where it travels fastest
d. in the medium where it travels fastest, moving towards the medium where it travels slowest
2. Total internal reflection is most likely to occur when ______.
a. the angles of incidence are smaller (e.g., close to 0 degrees)
b. the angles of incidence are greatest (e.g., close to 90 degrees)
Complete the following blanks by answering questions #3-#4:
The critical angle is the angle of (#3)
which causes light to
3. Referring to the statement above:
a. incidence b. refraction c. reflection
4. Referring to the statement above:
a. cross the boundary without refracting
b. undergo refraction at the same angle as the angle of incidence
c. refract at an angle of refraction of 90 degrees
d. reflect at the same angle as the angle of incidence
(#4) .
The next three questions focus on the brightness of the reflected and refracted rays and the
dependency
of the brightness upon the angle of incidence.
5. Consider the diagram at the right for rays A, B, C, and D incident upon a water-air
boundary. The corresponding refracted rays are shown. Draw the corresponding reflected
rays and label them as A'', B'', C'', and D''.
6. As the angle of incidence is gradually increased, more and more of the energy from the
incident ray goes into the reflected ray, while less and less of the energy goes into the
refracted ray. Based on this fact, which one of the refracted rays in the diagram would be
brightest and which one would be dimmest?
Brightest: _____Dimmest: _____
7. For incident ray C, the angle of refraction is 90°. The refracted ray C has the smallest amount of energy of any refracted ray. Thus, it would
be an extremely "dim" light ray. What is the angle of incidence for ray C called?
8. The critical angle for an air (n=1.0) - lucite (n=1.4) boundary is approximately 46 degrees. Which of the following diagrams depict
incident rays which would undergo total internal reflection (TIR) at the angle shown? Circle all that apply. A B C D
9. Calculate the critical angle for the ....
a. ... air (n = 1.00) - water (n = 1.33) boundary:
b. ... air (n = 1.00) - diamond (n = 2.42) boundary:
c. ... water (n = 1.33) - glass (n = 1.50) boundary:
10. a. Calculate the critical angle for the boundary between glass (n = 1.50) and diamond (n = 2.42). PSYW
b. On the diagram at the right, draw an incident ray that approaches the boundary with an angle equal to the critical
angle. Label the incident ray as A. Draw the corresponding refracted ray and label the ray as B.
c. Draw an incident ray which would approach the boundary at an angle greater than the critical angle. Label this
incident ray as C.
11. Diamonds are usually cut with a shape similar to that shown at the right. Kent
Affordit is preparing to propose to Amanda Befrendswyth. In an effort to save
money, Kent asked the jeweler to remove the bottom portion of the gem. Kent
reasoned that since it was not visible, its removal would have little consequence to
its ultimate appearance. Explain why Kent never did get engaged to Amanda.
Finally, draw the path of the given incident ray in each diamond.
Lenses
Read from Lesson 5 of the Refraction and Lenses chapter at The Physics Classroom: http://www.physicsclassroom.com/Class/refrn/u14l5a.html
http://www.physicsclassroom.com/Class/refrn/u14l5b.html
http://www.physicsclassroom.com/Class/refrn/u14l5c.html
1. Converging lenses are _____ at the center and _____ at the edges.
a. thickest, thinnest b. thinnest, thickest
2. Diverging lenses are _____ at the center and _____ at the edges.
a. thickest, thinnest b. thinnest, thickest
Consider the diagram at the right in answering the next two questions.
3. List the letters of all the converging lenses.
4. List the letters of all the diverging lenses.
'
5. Use refraction principles to sketch an approximate path of light as it enters and exits the lens. Think FST and SFA. Trace the path of the
rays into, through and out of the lens. Repeat the procedure for the light rays exiting the lens and trace the emerging light rays. Place
arrowheads on all light rays.
6. Explain why lenses (like the one on the left above) are called "converging" lenses.
7. Converging lenses will have ____________________ (positive, negative) focal lengths. Diverging lenses will have
____________________ (positive, negative) focal lengths.
8. The diagram below shows an arrow object positioned in front of a converging and a diverging lens.
Three incident rays are shown. Construct the corresponding refracted rays. Show arrowheads.
9. State the three rules of refraction for converging lenses:
#1:
#2:
#3:
10. State the three rules of refraction for diverging lenses:
#1:
#2:
#3:
11. The diagrams below depict the refraction of light through various lenses. List the diagrams that show the proper refraction of light.
_________ For those which show the improper refraction of light, either correct the diagrams by showing the proper refracted rays or
explain what is wrong with the refracted rays.
Ray Diagrams for Converging Lenses
Read from Lesson 5 of the Refraction and Lenses chapter at The Physics Classroom:
http://www.physicsclassroom.com/Class/refrn/u14l5da.html http://www.physicsclassroom.com/Class/refrn/u14l5db.html
For the following lenses and corresponding object positions, construct ray diagrams. Then describe the Location of the image, Orientation
(upright or inverted) of the image, the relative Size of the image (larger or smaller than object), and the Type of image (real or virtual). For
Case 4, merely construct the ray diagram.
Case
1: If the object is located beyond 2F:
Description of Image:
Location:
O: Upright or Inverted
S: Magnified or Reduced
T: Real or Virtual
S: Magnified or Reduced
T: Real or Virtual
S: Magnified or Reduced
T: Real or Virtual
Case 2: If the object is located at 2F:
Description of Image:
Location:
O: Upright or Inverted
Case 3: If the object is located between 2F and F:
Description of Image:
Location:
O: Upright or Inverted
Case 4: If the object is located at F:
No Description Required
Case 5: If the object is located between F and the lens:
Description of Image:
Location:
O: Upright or Inverted
S: Magnified or Reduced
T: Real or Virtual
Ray Diagrams for Diverging Lenses
Read from Lesson 5 of the Refraction and Lenses chapter at The Physics Classroom: http://www.physicsclassroom.com/Class/refrn/u14l5ea.html
http://www.physicsclassroom.com/Class/refrn/u14l5eb.html
For the following lenses and corresponding object positions, construct ray diagrams. Then describe the Location of the image, Orientation
(upright or inverted) of the image, the relative Size of the image (larger or smaller than object), and the Type of image (real or virtual).
Case 1: If the object is located far away from the lens:
Description of Image:
Location:
O: Upright or Inverted
S: Magnified or Reduced
T: Real or Virtual
Case 2: If the object is located nearby the lens:
Location:
O: Upright or Inverted
S: Magnified or Reduced
T: Real or Virtual
Lenses and Mirrors - Applying Concepts
1. Light emanates in a variety of directions from the following point objects; some of this light is incident towards the mirror or lens. The
behavior of a few such incident rays is shown below.
Show how the third, fourth and/or fifth incident rays refract or reflect.
2. Several statements about images are given below. Identify which optical device applies to the given statement. Place the appropriate marks
in the blanks. Mark all that apply.
A = plane mirrors B = concave mirrors C = convex mirrors D = converging lenses E = diverging lenses
_____ a. Are capable of producing real images.
_____ b. Only produce virtual images.
_____ c. Are capable of producing enlarged images.
_____ d. Can only produce images which are smaller than the object.
_____ e. Capable of producing images the same size as the object.
3. Identify the following statements as being either true (T) or false (F).
_____ a. If reflected or refracted rays diverge, there is no image.
_____ b. If an object is located in front of a focal point, there is no image.
_____ c. Virtual images cannot be seen.
_____ d. All images are formed by the actual convergence of reflected or refracted light.
_____ e. Just three rays of light from an object can intersect at the image location.
Lens Practice
Read from Lesson 5 of the Refraction and Lenses chapter at The Physics Classroom: http://www.physicsclassroom.com/Class/refrn/u14l5f.html
Use the lens equation and magnification equation to solve the following problems.
1. Determine the image distance and image height for a 4.0-cm tall object placed 54.0-cm from a converging lens having a focal length of
18.0 cm.
2. Determine the image distance and image height for a 4.0-cm tall object placed 36.0-cm from a converging lens having a focal length of
18.0 cm.
3. Determine the image distance and image height for a 4.0-cm tall object placed 24.0-cm from a converging lens having a focal length of
18.0 cm.
4. Determine the image distance and image height for a 4.0-cm tall object placed 12.0-cm from a converging having a focal length of 18.0
cm.
5. A magnified, inverted image is located a distance of 32.0 cm from a converging lens with a focal length of 12.0 cm. Determine the object
distance and tell whether the image is real or virtual.
6. ZINGER: An inverted image is magnified by 2 when the object is placed 22 cm in front of a converging lens. Determine the image
distance and the focal length of the lens.
7. A diverging lens has a focal length of -12.8 cm. An object is placed 34.5 cm from the lens's surface. Determine the image distance.
8. Determine the focal length of a diverging lens which produces an image which is 12.9 cm behind the lens when the object is 32.4 cm from
the lens.
9. A 2.85-cm diameter coin is placed a distance of 31.4 cm from a diverging lens which has a focal length of -11.6 cm. Determine the image
distance and the diameter of the image.
10. The focal point is located 20.0 cm from a diverging lens. An object is placed 12.0 cm from the lens. Determine the image distance.
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