1. PHYSICS InClass by SSL Technologies with S. Lancione Exercise-52
High School
Optics
InClass
by SSL Technologies
with S. Lancione
Exercise-52
Lenses
Part 1 /2

2. Lenses Convex Concave PART-1 /2 LENSES
Whereas mirrors produce images by reflection, lenses produce
images by refraction. Depending upon their “thickness”, lenses are classified as “thick” or “thin”. In this course, we will only consider “thin” lenses. In effect, therefore, we disregard the thickness of the lens assuming it to be a line.
Convex
Concave
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3. Lenses
PART-1
There are two main types of lenses called convex (also known as converging ) and concave (also known as diverging ).
Convex lenses are thicker in the middle than at the edges while
concave lenses are thicker at the edges than in the middle.
As illustrated below, both convex and concave lenses each have
three variations.
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4. Lenses PART-1 Convex Lens Concave Lens
When representing “thin” lenses in a diagram, it is sometimes more
convenient to simply draw an arrow rather than the actual lens.
Using this method, an arrow is used to represent the lens as
illustrated below.
Convex Lens
Concave Lens
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5. Convex lenses are thicker in the middle and thus converge light rays.
REMEMBER
Convex lenses are thicker in the middle and thus converge light rays.
Concave lenses are thinner in the middle and thus diverge light rays.
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6. Lenses
PART-1
Just as with concave mirrors, the characteristics of the image
formed by a converging lens depend upon the location of the object.
There are six "strategic" locations where an object may be placed.
For each location, the image will be formed at a different place and
with different characteristics. We will illustrate the six different
locations and label them as CASE-1 to CASE-6.
Case-1: Object at infinity
Case-2: Object just beyond 2 F’
Case-3: Object at 2F’
Case-4: Object between 2F’ and F’
Case-5: Object at F’
Case-6: Object within focal length (f)
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7. Convex (converging) Lenses CASE-1 : Object at “infinity”
Infinity simply means
“far away”.
CASE-1 : Object at “infinity”
No image
Object
NOTE
Since the object is at “infinity”,
all rays arrive parallel.
No image formed (All rays pass through F)
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8. Convex (converging) Lenses CASE-2 : Object just beyond 2F’
NOTE
In order to establish an image point, all we need are two intersecting rays.
CASE-2 : Object just beyond 2F’
Note-1
A ray that comes parallel
is refracted through F.
Note-2
A ray that goes through the
vertex goes right through.
Note-3
A ray that goes through F’
is refracted parallel.
Object
Image
This ray is extra in locating the image.
Image is real (formed by refracted rays)
Inverted (upside down)
Reduced (smaller than object)
Located between F and 2F
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9. Convex (converging) Lenses CASE-3 : Object at 2F’
Again:
In order to establish an image point, all we need are two intersecting rays.
CASE-3 : Object at 2F’
Object
Image
This ray is extra.
Image is real (formed by refracted rays)
Inverted (upside down)
Same size as object
Located at 2F
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10. Convex (converging) Lenses CASE-4 : Object between 2F’ and F’
Image
Image is real (formed by refracted rays)
Inverted (upside down)
Magnified (larger than object)
Located beyond 2F
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11. Convex (converging) Lenses CASE-5 : Object at F’ No image is formed
(rays refract parallel)
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12. Convex (converging) Lenses CASE-6 : Object is within focal length
Image
Object
Image is virtual
(formed by extended rays)
Upright
Magnified
Located on same side as object
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13. Now let's consider
Concave lenses
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14. Concave (diverging) Lenses One case only! Image is always virtual
Object
Image
Image is always virtual
(formed by a direct ray and an extended ray)
Always upright
Always reduced
Always located on same side as object
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15. Lenses
PART-1
Be sure to follow the following sign convention when solving problems concerning lenses.
 Sign convention:
1- Object distance is always positive.
2- Image distance is positive if the image is on the side of the
lens where light emerges (from lens).
3- Image distance is negative if the image is on the side of the
lens where the light enters (the lens).
4- The focal length of a convex (converging) lens is positive.
5- The focal length of a concave (diverging) lens is negative.
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16. EXERCISES

17. Question-1 Convex Converging
A lens that is thicker in the middle than at the ends is known as:
Convex
Converging
A lens or a lens.
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18. Question-2 Concave Diverging
A lens that is thicker at the ends than in the middle is known as:
Concave
Diverging
A lens or a lens.
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19. Question-3
Trace the rays that emerge from the following glass mediums: a) b) c) d)
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20. Question-4
For each case below, draw the appropriate lens that will produce
the indicated rays. a)
Concave (diverging) b)
Convex (converging)
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21. Question-5 A mirror forms an image by reflection whereas
How is the image formed by a mirror different from the image
formed by a lens?
A mirror forms an image by reflection whereas
a lens forms a an image by refraction.
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22. Image is real, inverted, reduced and located between F and 2F.
Question-6
For each convex lens illustrated below, draw the image. a)
Image
Image is real, inverted, reduced and located between F and 2F.
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23. Image is real, inverted, same size object and located at 2F.
Question-6
For each convex lens illustrated below, draw the image. b)
Image
Image is real, inverted, same size object and located at 2F.
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24. Image is real, inverted, magnified and located beyond 2F.
Question-6
For each convex lens illustrated below, draw the image. c)
Image
Image is real, inverted, magnified and located beyond 2F.
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25. All rays refract parallel,
Question-6
For each convex lens illustrated below, draw the image. d)
Parallel
All rays refract parallel,
no image is formed.
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26. Question-6 For each convex lens illustrated below, draw the image. e)
Image is virtual, upright, magnified and located on same side as object.
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27. Image is virtual, upright, reduced and located on same side as object.
Question-7
For each concave lens illustrated below, draw the image.
REMEMBER
Concave lenses always produce images that are virtual, upright and reduced.
Image
Image is virtual, upright, reduced and located on same side as object.
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28. Image is virtual, upright, reduced and located on same side as object.
Question-7
For each concave lens illustrated below, draw the image.
Image
Image is virtual, upright, reduced and located on same side as object.
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29. Question-8 Real 60 cm - 3 (inverted and 3x larger than object) 21 cm
An object that is 7 cm high is placed 20 cm in front of a convex (converging) lens whose focal length is 15 cm. Determine the
characteristics of the image:
Real
Type (real or virtual): _______________
Location: _______________
Magnification: _______________
Height: _______________
60 cm
- 3 (inverted and 3x larger than object)
21 cm
Negative sign indicates inversion.
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30. Note that diverging lenses have a negative focal length.
Question-9
An object whose height is 4 cm is placed 50 cm from a concave
(diverging) lens. If the focal length of the lens is 30 cm, determine
the characteristics of the image:
Virtual
Type (real or virtual): _______________
Location: _______________
Magnification: _______________
Height: _______________
18.75 cm
0.375 (upright and smaller than object)
1.5 cm
Note that diverging lenses have a negative focal length.
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31. Question-10 Real 28 cm - 0.04 (inverted and smaller than object) 2 cm
An object that is 5 cm high is placed 70 cm in front of a convex
(converging) lens whose focal length is 20 cm. Determine
the characteristics of the image:
Real
Type (real or virtual): _______________
Location: _______________
Magnification: _______________
Height: _______________
28 cm
(inverted and smaller than object)
2 cm
Negative sign indicates inversion.
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32. Question-11 A lens produces the following optical effect.
Which group of lens produces the above effect?
Plano convex D)
Double convex C)
Plano concave B)
Double concave A)
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33. Question-12
Beams of light rays are traveling through air parallel to the principal axis of four different lenses. The light rays enter the lenses and are refracted.
In which diagram are the light rays correctly illustrated?
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