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Go to Answers to Refraction Problems (revised 04-10-03)
REFRACTION
Sample
Solutions
1. A 68 m focal length converging lens forms an
image that is one-fourth the size of the object. (A) What must
be the object distance? (B) What will be the resulting image distance?
(1/P) + (1/Q) = (1/F); (1/P) +
(1/(1/4P)) = (1/68 m)
(1/P) + (4/P) = (1/68 m); (5/P) =
(1/68 m); P = 340 m
Q = (1/4)P = (1/4)(340 m) = 85 m
2. An inverted and reversed image 3/5th the size of the
object is observed with a lens. The object and
An inverted, reversed and smaller image with lenses is a real image; therefore, a
convex (converging) lens must be used.
Q = 93/5)P; P + Q = 15 ft; P + (3/5)P = 15 ft; 5P + 3p = 15 ft; 8P = 75 ft;
P = 9.375 ft;
Q = (3/5)P = (3/5)(9.375 ft) = 5.625 ft
(1/P) + (1/Q) = (1/F); (1/F) = (1/9.375 ft) + (1/5.625 ft); F = 3.5156 ft
3. An upright and regular image that is 6/5th the size
of the object is observed with a lens when the
An upright, regular and larger image with lenses
is a virtual image and a convex (diverging) lens
P =
34 ft; Q = (6/5)P = (6/5)(34 ft) = 40.8 ft; Q will be -40 m because it is virtual
(1/F) = (1/P) + (1/Q); (1/F) = (1/34 ft) + (1/(-40.8 ft)); F = 204 ft
Problems
1. A converging lens has a principal focal length of 30
cm. Calculate the image distances for the following
object distances:
(A) 10 cm
(B) 20 cm
(C) 30 cm
(D) 40 cm
(E) 60 cm.
2. A converging lens has a principal focal length of 20
cm. What must be the object distance to produce,
(A) a real image that is twice the size of the object?
(B) a virtual image that is three times the size of the object?
3. A converging lens has a principal focal length of 24
cm. What must be the object distance to produce,
(A) an inverted image that is three times as large as the object?
(B) a virtual image that is magnified 5 times?
4. What distance in front of a converging lens, in terms
of the principal focal length, must an object
5. The distance between an object and its real image,
formed by a converging lens, is 120 cm.
(A) What
is the focal length of the lens if the image is magnified two times?
(B) What must be the object distance?
(C) What will be the resulting image
distance?
6. A diverging lens forms an image of an object that is
located 20 cm from the lens. The focal length
(A) What is the image distance?
(B) Describe the image?
7. An object is located 20 cm from a lens. An upright
image that is one-half the size of the object is
(A) What type of lens is required?
(B) What must be the focal length?
8. A 20 cm focal length converging lens is placed 50 cm
from the object.
(A) What is the image distance?
(B) Describe the image?
9. An object is 10 inches from a 5 inch focal length
converging lens.
(A) What is the image distance?
(B) Describe the image?
10. A 10 cm focal length lens with a fixed image
distance of 11 cm is used in a basic box camera. How far
away must the object be located so that it will be clearly focused on the film?
11. A 3 inch tall object is placed 20 inches from a
converging lens. A real image is formed 10
inches from the lens.
(A) What is the focal length of the lens?
(B) What will be the image size?
12. An object is located 30 cm from a converging lens
that forms a real image 5 cm tall and 60 cm
(A) What is the focal length of the
lens?
(B) What is the size of the image?
13. A converging lens forms a real image that is four
times the size of the object. The image is located
(A) What is the object distance?
(B) What is the image distance?
14. You observe an image 4 cm from its object. The image
is observed to be three-fourth the size of the
object.
(A) What is the object distance?
(B) What is the image distance?
15. A real image that is four times the size of the
object is separated from the object by a distance of
(A) What is the object distance?
(B) What is the image distance?
(C) What is the focal length of the
lens?
16. An object 5 cm high is located 12 cm in front of a 8
cm focal length lens.
(A) What is the image distance?
(B) What is the image size?
17. An object 3 inches tall is located 20 inches from a
12 inch focal length converging lens.
(A) What is the image distance?
(B) What is the image size?
18. A 2 ft tall object is located 10 ft from a 6 ft
focal length diverging lens.
(A) What is the image size?
(B) What is the image distance?
19. A 12 cm focal length lens is located so that it
forms an image that is four times the size of the object.
(A) What is the object distance?
(B)
If this same lens is to produce a virtual image six times the size of the object, what must be the
(C) Find the image distances for BOTH part (A & B).
(D) What type of lens is needed for BOTH “A” and “B”?
20. A growing flower is planted 9 ft from a wall. Where
should a 2 ft focal length lens be placed to form a
21. A 30 cm focal length lens is used to form an image
on a screen that is located 150 cm from the
22. An object 2 ft tall is located 10 ft in front of a 6
ft converging lens.
(A) What is the image size?
(B) What is the image location?
23. An object 3 inches tall is located in front of a 12
inch focal length lens.
(A) What is the image size?
(B) What is the image location?
24. (deleted)
25. The distance between and object and its real image,
formed by a lens is 120 cm. The image is to be
(A) What focal length lens must be
used?
(B) What must be the object distance?
(C) What will be the resultant image
distance?
26. The distance between and object and its virtual
image, formed by a lens is 120 cm. The image is to be
three times the size of the object.
(A) What focal length lens must be used?
(B) What must be the object distance?
(C) What will be the resultant image
distance?
27. Light strikes the surface of flint glass (n = 1.517)
from air (n = 1) at an angle of 57o as it passes into glycerol (n = 1.475) and then into water (n =
1.33). With what angle will the light emerge into water
28. What minimum angle is required to obtain internal
reflection when light passes from acetone
29. What is the critical angle if light is to pass
between glycerol (n = 1.47) and quartz (n = 1.544)? In
30. (A) Where must one place an object to observe a
reversed image seven-fifth the size of the object if
(B) What type of lens is required?
(C) What is the object and image distances respectively?
USE ALL POSSIBLE SITUATIONS
31. An inverted image is observed at a point 56 feet
from the object. If the focal length of the lens is 12 ft,
(A) what is(are) the possible location(s) for
the object from the lens?
(B) What will be the respective image
location ?
USE ALL POSSIBLE SITUATIONS
32. We wish to observe an image with a lens where the
object is five times the size of the image. The lens we are given has a focal length of 54 cm.
(A) What type of lens is it?
(B) What is(are) the possible object
location(s)?
(C) What is(are) the possible image
location(s)?
USE ALL POSSIBLE SITUATIONS
33. An
upright image and its object are separated by a distance of 14 meters.
(A) What focal length lens is
required if the object is to be two-thirds the size of the image?
(B) What are the possible object and
image distances?
(C) What are the possible object
locations?
35. For the same soap bubble of 220.0 nm thickness, what wavelength of incident light will give maximum reflection within the visible portion of the electromagnetic spectrum? Why must "m" be given a value of "1"? What wavelength of light corresponds to an "m" of "0"? For an "m" of "2"? (visible spectrum = 380.0 - 720.0 nm)
36. What thickness of magnesium fluoride (MgF2, n = 1.38) should be deposited on a glass lens of ng = 1.50, such that the greatest portion of incident white light should not be reflected?
37. For the same coated glass lens used above, what wavelength within the visible spectrum will give maximum reflection of light?
38. A thin film of gasoline floats on a puddle of water. Sunlight falls almost perpendicularly on the film and reflects into your eyes. Although sunlight is white, since it contains all colors, the film has a yellow hue, because destructive interference eliminates the color of blue (lambda vacuum = 469 nm) from the reflected light. If the refractive indices of blue light in gasoline and water are 1.40 and 1.33, respectively, determine the minimum nonzero thickness "d" of the film.
39. Calculate the minimum thickness of a soap bubble (n = 1.33) that will result in constructive interference in the reflected light if the film is illuminated with light whose wavelength in air is 600 nm.
40. Solar cells are often coated with a transparent thin film of silicon monoxide (SiO, n = 1.45), in order to minimize reflective losses from the surface. A silicon solar cell (n = 3.50) is coated with a thin film of silicon monoxide for this purpose. Determine the minimum thickness of the film that will produce the least reflection of white light.
SELF-TEST
Multiple
Choice:
1. Light can travel 1.86 x 108 miles in:
(A)
1 sec
(C) 100 sec
(B)
10 sec
(D) 1,000 sec
2. The image of an object IS NOT inverted
in:
(A)
an eye
(C) a pinhole camera
(B)
a reading lens
(D) a slide projector
3. In almost every field of science, the instrument used
to see objects too small for the unaided eye is the:
(A)
telescope
(C) enlarger
(B)
spectroscope (D)
microscope
4. The bending of light rays as they pass from one
substance to another is:
(A)
reflection
(C) refraction
(B)
absorption
(D) transmission
5. The defect observed because a single lens does not
focus all colors at the same place is:
(A)
depth of focus
(C) spherical aberration
(B)
index of refraction
(D) chromatic aberration
6. (deleted)
7. (deleted)
8. In the tank of water in the following diagram, the
incident ray of light would strike the bottom at which
(A)
A
(C) C
(B)
B
(D) D
9. (deleted)
10. Virtual images are formed whenever the distance of
an object from a lens is less than:
(A) 1 ft
(C) twice the focal length
(B) 2 ft
(D) none of the above
11. (deleted)
12. As light goes from air into diamond, it is:
(A) slowed down
(C) totally refracted
(B) speeded up
(D) totally reflected
13. A girl 3 ft from a plane mirror is separated from
her image by a distance of:
(A) 3 ft
(C) 9 ft
(B) 6 ft
(D) 12 ft
Study the accompanying diagram carefully and then answer questions #14 - #16.
14. As the object is moved closer to “F”, the
new image is, as compared to the original image in the
(A) larger
(C) upright
(B) smaller
(D) the same size
15. The focal length of the lens is the distance from
the lens axis to:
(A) the object
(C) F’
(B) the image
(D) 2F’
16. If the image can be focused on a screen, it must be:
(A) upright
(C) reversed
(B) regular
(D) colored
17. (deleted)
18. (deleted)
19. An object is placed between “F” and
“2F” of a converging lens, the image formed will be:
(A) real and enlarged
(C) virtual and enlarged
(B) virtual and reduced
(D) real and reduced
20. When a beam of light passes from one medium into a
less dense medium, the angle of refraction is:
(A) greater than the angle of incidence
(C) equal to the angle of incidence
(B) less than the angle of incidence (D)
independent of the angle of incidence
21. The image formed by a diverging lens is:
(A) virtual and reduced
(C) real and enlarged
(B) virtual and enlarged
(D) real and inverted
22. To produce a parallel beam of light using a
converging lens, a lighted object must be placed at:
(A) a distance “2F” from the lens
(C) a distance of more than “2F” from the lens
(B) a distance “F” from the lens
(D) a distance of less than “F” from the lens
23. All incident parallel light rays do not pass through
the principal focus of a converging lens. This
A) spherical aberration
(C) chromatic aberration
(B) astigmatism
(D) binocular vision
24. Real images formed by a lens are:
(A) never on the same side of the lens as the object
(B) always on the same side of the lens as the object
(C) sometimes on the same side as the object
(D) maybe upright
25. When an object is placed at a distance of
“2F” from a converging lens, the
image is:
(A) reduced
(C) same size as the object
(B) enlarged
(D) non-existent
26. The image formed by a converging lens is never:
(A)
virtual and upright (C) virtual and enlarged
(B)
real and inverted
(D) virtual and reduced
27. If an object is between “F” and the
optical center, the image will be:
(A) at the principal focus
(E) between “F’ “ and “2F’ “ from the lens
(B) more than “2F’ “ from the lens
(F) at infinity
(C) on the same side of the lens as
the object
(D) “2F’ “ from the lens
28. If the distance of an object from a double convex
lens increases, the distance of the real image:
(A) does not change
(B) increases
(C) decreases
29. Referring to a convex lens, if the object is at
“2F”, the image will be:
(A) at the principal focus
(D) “2F’ “ from the lens
(B) more than “2F’ “ from the lens
(E) between “F’ “ and “2F’ “ from the lens
(C) on the same side of the lens as
the object (F)
at infinity
30. An object is placed between a convex lens and its
focal point. Indicate ALL of the following which will describe the image:
(A) upright
(D) diminished
(B) inverted
(E) real
(C) enlarged
(F) virtual
31. If an object is at an infinite distance from a
convex lens, the image will be found:
(A) at the principal focus
(D) “2F’ “ from the lens
(B) more than “2F’ “ from the lens
(E) between “F’ “ and “2F’ “ from the lens
(C) on the same side of the lens as the object
(F) at infinity
32. An object is placed between “F” and
“2F” from a convex lens. Indicate ALL of the following which will
describe the image:
(A) upright
(D) enlarged
(B) real
(E) diminished
(C) inverted
(F) virtual
33. When using a concave lens, the image is:
(A) upright, virtual and enlarged
(C) upright, real and diminished
(B) inverted, real and diminished
(D) upright, virtual and diminished
34. An object is placed at a distance greater than
“2F” from a convex lens. Indicate ALL of the following which
describe the image:
(A)
upright
(B)
inverted
(C)
enlarged
35. You are looking into a swimming pool at an oblique
angle while standing at the diving end. You
are
(A) over-estimate the depth of the water
(B) under-estimate the water depth
(C) correctly estimate the depth
Matching: Choose the term in the left-hand column that BEST
completes the statement or answers the question in the right-hand column.