Refraction and Lenses Review

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21. Dispersion occurs when _____.

  1. some materials bend light more than other materials
  2. a material slows down some colors more than others
  3. a material changes some colors more than others
  4. light has different speeds in different materials

 

Answer: B

Dispersion occurs when a single material bends certain colors of light more than other colors of light. The cause is the fact that different colors of light have different speeds within the same material.



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Dispersion of Light by Prisms

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22. A 3.0 cm tall object is placed along the principal axis of a thin converging lens of 30.0 cm focal length. If the object distance is 40.0 cm, which of the following best describes the image distance and height, respectively?

a. 17.3 cm and 7.0 cm

b. 120. cm and -9.0 cm

c. 17.3 cm and 1.3 cm

d. 120. cm and -1.0 cm


Answer: B

Use the lens equation:

1/di + 1/do = 1/f

where do = 40.0 cm and f = 30.0 cm. Solve for di.

1/di = 1/f - 1/do =1/(30.0 cm) - 1/(40.0 cm) = 0.00833 /cm

di = 1/(0.00833 /cm) = 120. cm

Then use the -di/do = hi/ho to find hi

It is now known that ho = 3.0 cm; do = 40.0 cm; di = 120. cm. Substitute and solve.

hi = -ho *(di/do) = -(3.0 cm) *(120. cm)/(40.0 cm) = -9.0 cm


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The Mathematics of Lenses


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23. Which of the following best describes the image for a thin converging lens that forms whenever the object is at a distance less than one focal length from the lens?

a. inverted, enlarged and real

b. upright, enlarged and virtual

c. upright, reduced and virtual

d. inverted, reduced and real


Answer: B

When an object is located inside of the focal point of a converging lens, the image will be virtual, upright, larger than the object and located on the same side of the lens as the object. In essence, the lens would serve as a magnifying glass.



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Ray Diagrams || Object-Image Relations


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24. Which of the following best describes the image for a thin diverging lens that forms whenever the magnitude of the object distance is less than that of the lens' focal length?

a. inverted, enlarged and real

b. upright, enlarged and virtual

c. upright, reduced and virtual

d. inverted, reduced and real



Answer: C

A diverging lens always produces an image with the same characteristics, regardless of the object distance. The image is always virtual, upright and reduced in size.

 

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Ray Diagrams || Object-Image Relations


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25An object is placed at a distance of 30.0 cm from a thin converging lens along its axis. The lens has a focal length of 10.0 cm. What are the values  of the image distance and magnification (respectively)?

a. 60.0 cm and 2.00

b. 15.0 cm and 2.00

c. 60.0 cm and -0.500

d. 15.0 cm and -0.500


Answer: D

Use the lens equation:

1/di + 1/do = 1/f

where do = 30.0 cm and f = 10.0 cm.

Solve for di :

1/di = 1/f - 1/do = 1/(10.0 cm) - 1/(30.0 cm) = 0.0666/cm

di = 1 / (0.0666/cm) = 15.0 cm

Then use the M =-di/do to find M

(do = 30.0 cm; di = 15.0 cm)

Substitute and solve for M:

M = -(15.0 cm) / (30.0 cm) = - 0.500


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The Mathematics of Lenses

  
 
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26. An object is placed at a distance of 6.0 cm from a thin converging lens along its axis. The lens has a focal length of 9.0 cm. What are the values, respectively, of the image distance and magnification?

a. -18 cm and 3.0

b. 18 cm and 3.0

c. 3.0 cm and -0.50

d. -18 cm and -3.0



Answer: A

Use the lens equation:

1/di + 1/do = 1/f

where do = 6.0 cm and f = 9.0 cm.

Solve for di:

1/di = 1/f - 1/do = 1/(9.0 cm) - 1/(6.0 cm) = -0.0556/cm

di = 1 / (-0.0556/cm) = -18 cm

Then use the M =-di/do to find M (do = 6.0 cm; di = -18 cm)

Substitute and solve for M:

M = -(-18 cm) / (6.0 cm) = 3.0


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The Mathematics of Lenses


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27. An object is placed at a distance of 30.0 cm from a thin converging lens along the axis. If a real image forms at a distance of 10.0 cm from the lens, what is the focal length of the lens?

a. 30.0 cm

b. 15.0 cm

c. 10.0 cm

d. 7.50 cm



Answer: D

Use the lens equation:

1/di + 1/do = 1/f

where do = 30.0 cm and di = 10.0 cm.

Solve for f:

1/f = 1/di + 1/do = 1/(10.0 cm) + 1/(30.0 cm) = 0.133/cm

f = 1 / (0.133/cm) = 7.50 cm



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The Mathematics of Lenses


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28. An object is placed at a distance of 40.0 cm from a thin lens along the axis. If a virtual image forms at a distance of 50.0 cm from the lens, on the same side as the object, what is the focal length of the lens?

a. 22.2 cm

b. 45.0 cm

c. 90.0 cm

d. 200. cm


Answer: D

Use the lens equation:

1/di + 1/do = 1/f

where do = 40.0 cm and di = -50.0 cm (Note that di is a negative number since it is a virtual image - i.e., formed on the same side of the lens as the object.)

Solve for f:

1/f = 1/di + 1/do = 1/(-50.0 cm) + 1/(40.0 cm) = 0.00500/cm

f = 1 / (0.00500/cm) = 200. cm



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The Mathematics of Lenses


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Part B: Multiple-Multiple Choice

29. Which of the following statements are true of converging lenses? Identify all that apply.

  1. Converging lenses are thicker at the center than they are at the edges.
  2. If the bottom half of a converging lens is covered, then the top half of the image will not be visible.
  3. Converging lenses only produce real images.
  4. Converging lenses can produce images which are both magnified and reduced in size.
  5. Converging lenses only produce inverted images.
  6. Converging lenses have a + focal length.
  7. The images formed by a converging lens can be located on either side of the lens relative to the object.

 

Answer: ADFG

  1. This is the basic physical feature that characterizes all converging lenses.
  2. Find a pair of eyeglasses and see if you can test the truth of this statement. Covering half the lens will only have the effect of making the image fainter.
  3. Converging lenses will produce a virtual image of an object placed in front of F.
  4. Converging lenses produce magnified images when the object is in front of 2F and reduced images when the object is behind 2F.
  5. Converging lenses can produce upright images of objects placed in front of F.
  6. Focal length is + for converging lenses and - for diverging lenses.
  7. Converging lenses produce both real images formed on the opposite side of the lens (when the object is placed beyond F) and virtual images formed on the same side of the lens (when the object is placed in front of F).


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The Anatomy of a Lens || Converging Lenses - Object-Image Relations


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30. Which of the following statements are true of diverging lenses? Identify all that apply.

  1. Diverging lenses are thicker at the center than they are at the edges.
  2. If the bottom half of a diverging lens is covered, then the bottom half of the image will not be visible.
  3. Diverging lenses only produce virtual images.
  4. Diverging lenses can produce images which are both magnified and reduced in size.
  5. Diverging lenses only produce upright images.
  6. Diverging lenses have a - focal length.
  7. The images formed by a diverging lens can be located on either side of the lens relative to the object.

Answer: CEF

  1. Diverging lenses would be thinner at the center and thickest along the top and bottom edges.
  2. Just like the case of a converging lens, if half of a diverging lens is covered, the full image is still seen; it is merely fainter.
  3. Always. A real image is never produced by a diverging lens.
  4. Diverging lenses only produce one type of image - a virtual image which is upright and reduced in size.
  5. See above statement.
  6. Diverging lenses have a - focal length and converging lenses have a + focal length.
  7. Diverging lenses only produce virtual images; these images are located on the object's side of the lens.


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The Anatomy of a Lens || Diverging Lenses Object-Image Relations


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31. Which of the following statements are true of real images? Identify all that apply.

  1. Real images are inverted.
  2. Real images as formed by lenses are located on the opposite side of the lens from the object.
  3. Real images are magnified in size.
  4. Real images are only formed by converging lenses, never by diverging lenses.
  5. An image of a real object is formed; the image distance (s' or di) for real images is a + value.
  6. An image of a real object is formed; the image height (h' or hi) for real images is a + value.
  7. Real images have a - magnification value.

Answer: ABDEG

  1. This is always the case - real images are inverted and virtual images are upright.
  2. Real images are always located on the opposite side of the lens; virtual images are located on the object's side of the lens.
  3. Real images can be either magnified (converging lens, object between F and 2F), reduced (converging lens, object beyond 2F), or the same size (converging lens, object at 2F) as the object.
  4. Diverging lenses can only produce virtual images; converging lenses can produce both virtual and real images.
  5. Real images - those formed on the opposite side of the lens have a positive s' value (seep. 789 for more).
  6. Real images are inverted; this corresponds to a negative h' value.
  7. Real images are inverted; this corresponds to a negative magnification value.


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Converging Lenses - Object-Image Relations || Diverging Lenses Object-Image Relations || The Mathematics of Lenses


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32. Which of the following statements are true of virtual images? Identify all that apply.

  1. Virtual images are always upright.
  2. Virtual images as formed by lenses are always located on the same side of the lens as the object.
  3. Virtual images are only formed by diverging lenses, never by converging lenses.
  4. Virtual images are always smaller than the object.
  5. An image of a real object is formed; the image distance (s' or di) for virtual images is a - value.
  6. An image of a real object is formed; the image height (h' or hi) for virtual images is a - value.
  7. Virtual images have a - magnification value.

Answer: ABE

  1. Virtual images, whether formed by mirrors (of any type) or lenses, are always upright; real images are always inverted.
  2. Virtual images are always located on the object's side of the lens; real images are always located on the opposite side of the lens.
  3. Virtual images can be formed by both converging lenses (when the object is inside of F) and diverging lenses (regardless of the object location).
  4. Virtual images can be larger than the object (when formed by converging lenses) or smaller than the object (when formed by diverging lenses).
  5. Virtual images are located on the object's side of the lens; this corresponds to a negative s' value.
  6. Virtual images are always upright; this corresponds to a positive h' value.
  7. Virtual images are always upright; this corresponds to a positive M value.


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Converging Lenses - Object-Image Relations || Diverging Lenses Object-Image Relations || The Mathematics of Lenses


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33. Several characteristics of images are described below. Determine whether these images are real or virtual and whether they are formed by converging, diverging lenses or either type. (In all cases, assume that the object is an upright and real object.)

  1. Image is upright and magnified.
  2. Image if upright and reduced in size.
  3. Image is inverted and magnified.
  4. Image has a negative s' (di) value.
  5. Image has a negative h' (hi) value.
  6. Image has a positive h' (hi) value and a magnification value greater than 1.

Answer: See answers below

  1. Converging only; an upright (and virtual) and magnified image can only be formed when the object is between F and the surface of a converging lens. Diverging lenses would only produce upright images which are reduced in size.
  2. Diverging only; an upright (and virtual) and reduced image can only be formed by a diverging lens. When converging lenses produce upright images, they are magnified in size.
  3. Converging only; diverging lenses can only produce upright images which are reduced in size; an inverted and magnified image can be produced by a converging lens when the object is located between F and 2F.
  4. Both lenses; a negative s' value corresponds to a virtual image; both converging and diverging lenses can produce virtual images.
  5. Converging only; a negative h' value corresponds to an inverted (and real) image; only a converging lens can produce a real image.
  6. Converging only; a positive h' value corresponds to an upright (and virtual) image; the M > 1 statement indicates that the image is magnified. A magnified, upright, virtual image can only be produced by a converging lens when the object is between F and 2F.


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Converging Lenses - Object-Image Relations || Diverging Lenses Object-Image Relations || The Mathematics of Lenses


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34. Which of the following statements are true of total internal reflection (TIR)? Include all that apply.

  1. TIR can only occur when light approaches a boundary and is incident within the most dense media.
  2. TIR can only occur when the angle of incidence is greater than the critical angle.
  3. TIR causes a portion of the light to refract along the boundary and the rest to be reflected.
  4. When TIR occurs, the reflected light follows the law of reflection.
  5. If TIR occurs at the boundary of water and air, then the light must be within water and heading towards the boundary with air.
  6. If TIR occurs at the boundary of glass and air, then it is possible that the light is traveling within air and heading towards the glass.

Answer: ABE

  1. There are two conditions which must be met for TIR to occur; this is the first condition.
  2. This is the second condition.
  3. When TIR occurs, all (total) of the light reflects. There is no (nada, none, zero, zilch) refraction taking place.
  4. Yes! Reflection always follows the law of reflection. The angle of incidence equals the angle of reflection.
  5. TIR can only take place if the light is incident within the more dense of the two medium - in this case, water.
  6. Never; air is the least dense of the two media; this would violate the first of the two conditions for TIR. TIR would only take place at this boundary if the light was in the glass and heading towards the boundary with air.


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Total Internal Reflection || The Critical Angle


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