Ray Diagrams
J.M. Gabrielse
Outline
• Reflection
• Mirrors
• Plane mirrors
• Spherical mirrors
• Concave mirrors
• Convex mirrors
• Refraction
• Lense...
A ray of light is an extremely narrow
beam of light.

J.M. Gabrielse
All visible objects emit or reflect
light rays in all directions.

J.M. Gabrielse
Our eyes detect light rays.

J.M. Gabrielse
We see images when
light rays
converge in our eyes.

converge: come together
J.M. Gabrielse
Mirrors

It is possible to see
images in mirrors.
image

object
J.M. Gabrielse
Reflection
(bouncing light)
normal

Reflection is when light
changes direction by
bouncing off a surface.
When light is re...
Mirrors reflect light rays.

J.M. Gabrielse
Plane Mirrors
(flat mirrors)

How do we see images in
mirrors?

J.M. Gabrielse
Plane Mirrors
(flat mirrors)

object

image
How do we see images in
mirrors?

Light reflected off the mirror converges to ...
Plane Mirrors
(flat mirrors)

object

image
How do we see images in
mirrors?

Light reflected off the mirror converges to ...
Plane Mirrors
(flat mirrors)

object

image
How do we see images in
mirrors?

Light reflected off the mirror converges to ...
Spherical Mirrors
(concave & convex)

J.M. Gabrielse
Concave & Convex
(just a part of a sphere)

•
C

r
•
F
f

C: the center point of the sphere
r: radius of curvature (just t...
Concave Mirrors
(caved in)

•
F

optical axis

Light rays that come in parallel to the optical axis reflect through the fo...
Concave Mirror
(example)

•
F

optical axis

J.M. Gabrielse
Concave Mirror
(example)

•
F

optical axis

The first ray comes in parallel to the optical axis and reflects through the ...
Concave Mirror
(example)

•
F

optical axis

The first ray comes in parallel to the optical axis and reflects through the ...
Concave Mirror
(example)

•
F

optical axis

The first ray comes in parallel to the optical axis and reflects through the ...
Concave Mirror
(example 2)

•
F

optical axis

J.M. Gabrielse
Concave Mirror
(example 2)

•
F

optical axis

The first ray comes in parallel to the optical axis and reflects through th...
Concave Mirror
(example 2)

•
F

optical axis

The first ray comes in parallel to the optical axis and reflects through th...
Concave Mirror
(example 2)

•
F

optical axis

The first ray comes in parallel to the optical axis and reflects through th...
Concave Mirror
(example 2)

•
F

optical axis

The first ray comes in parallel to the optical axis and reflects through th...
Your Turn
(Concave Mirror)

object

•
F

optical axis

concave mirror
• Note: mirrors are thin enough that you just draw a...
Your Turn
(Concave Mirror)

object

•
F

optical axis

concave mirror
• Note: mirrors are thin enough that you just draw a...
Convex Mirrors
(curved out)

•
F

optical axis

Light rays that come in parallel to the optical axis reflect from the foca...
Convex Mirror
(example)

•
F

optical axis

J.M. Gabrielse
Convex Mirror
(example)

•
F

optical axis

The first ray comes in parallel to the optical axis and reflects through the f...
Convex Mirror
(example)

•
F

optical axis

The first ray comes in parallel to the optical axis and reflects through the f...
Convex Mirror
(example)

•
F

optical axis

The first ray comes in parallel to the optical axis and reflects through the f...
Convex Mirror
(example)

•
F

optical axis

The first ray comes in parallel to the optical axis and reflects through the f...
Your Turn
(Convex Mirror)

•
F

object

optical axis

convex mirror
• Note: mirrors are thin enough that you just draw a l...
Your Turn
(Convex Mirror)

object

image

•
F

optical axis

convex mirror
• Note: mirrors are thin enough that you just d...
Lensmaker’s Equation

1 1 1
= +
f di do
ƒ = focal length
do = object distance
di = image distance
if distance is negative ...
Magnification Equation

hi − di
m=
=
ho
do
m = magnification
hi = image height
ho = object height
If height is negative th...
Refraction
(bending light)
Refraction is when light bends as it
passes from one medium into another.

normal

air

θi

Whe...
Lenses
The first telescope, designed and built by Galileo, used lenses to focus light from
faraway objects, into Galileo’s...
Concave Lenses
Concave lenses are thin in the middle and make
light rays diverge (spread out).

•
F
optical axis

If the r...
Concave Lenses

•
F
optical axis

Light rays that come in parallel to the opticalignore the thickness offocallens.
The lig...
Concave Lenses

•
F

optical axis

Light rays that come in parallel to the optical axis still diverge from the focal point...
Concave Lens
(example)

•
F

optical axis

The first ray comes in parallel to the optical axis and refracts from the focal...
Concave Lens
(example)

•
F

optical axis

The first ray comes in parallel to the optical axis and refracts from the focal...
Concave Lens
(example)

•
F

optical axis

The first ray comes in parallel to the optical axis and refracts from the focal...
Concave Lens
(example)

•
F

optical axis

The first ray comes in parallel to the optical axis and refracts from the focal...
Your Turn
(Concave Lens)

object

•
F

optical axis

concave lens
• Note: lenses are thin enough that you just draw a line...
Your Turn
(Concave Lens)

object

•
Fimage

optical axis

concave lens
• Note: lenses are thin enough that you just draw a...
Convex Lenses
Convex lenses are thicker in the middle and focus light rays to a focal point in front of
the lens.

The foc...
Convex Lenses

•
F
optical axis

J.M. Gabrielse
Convex Lenses

•
F
optical axis

Light rays that come in parallel to the optical axis converge at the focal point.
J.M. Ga...
Convex Lens
(example)

•
F
optical axis

The first ray comes in parallel to the optical axis and refracts through the foca...
Convex Lens
(example)

•
F
optical axis

The first ray comes in parallel to the optical axis and refracts through the foca...
Convex Lens
(example)

•
F
optical axis

The first ray comes in parallel to the optical axis and refracts through the foca...
Convex Lens
(example)

•
F
optical axis

The first ray comes in parallel to the optical axis and refracts through the foca...
Your Turn
(Convex Lens)

•
F

object

optical axis
image

convex lens
• Note: lenses are thin enough that you just draw a ...
Your Turn
(Convex Lens)

•
F

object

optical axis
image

convex lens
• Note: lenses are thin enough that you just draw a ...
Thanks/Further Info
• Faulkes Telescope Project: Light & Optics by Sarah Roberts
• Fundamentals of Optics: An Introduction...
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  • When doing geometric optics problems it is much simpler to draw the lens/mirror as a line so that the light relects/refracts at the line. This saves us from having to show the lights behavior inside the lens.
  • 14 ray diagrams

    1. 1. Ray Diagrams J.M. Gabrielse
    2. 2. Outline • Reflection • Mirrors • Plane mirrors • Spherical mirrors • Concave mirrors • Convex mirrors • Refraction • Lenses • Concave lenses • Convex lenses J.M. Gabrielse
    3. 3. A ray of light is an extremely narrow beam of light. J.M. Gabrielse
    4. 4. All visible objects emit or reflect light rays in all directions. J.M. Gabrielse
    5. 5. Our eyes detect light rays. J.M. Gabrielse
    6. 6. We see images when light rays converge in our eyes. converge: come together J.M. Gabrielse
    7. 7. Mirrors It is possible to see images in mirrors. image object J.M. Gabrielse
    8. 8. Reflection (bouncing light) normal Reflection is when light changes direction by bouncing off a surface. When light is reflected off a mirror, it hits the mirror at the same angle (the incidence angle, θi) as it reflects off the mirror (the reflection angle, θr). The normal is an imaginary line which lies at right angles to the mirror where the ray hits it. reflected ray incident ray θr θi Mirror J.M. Gabrielse
    9. 9. Mirrors reflect light rays. J.M. Gabrielse
    10. 10. Plane Mirrors (flat mirrors) How do we see images in mirrors? J.M. Gabrielse
    11. 11. Plane Mirrors (flat mirrors) object image How do we see images in mirrors? Light reflected off the mirror converges to form an image in the eye. J.M. Gabrielse
    12. 12. Plane Mirrors (flat mirrors) object image How do we see images in mirrors? Light reflected off the mirror converges to form an image in the eye. The eye perceives light rays as if they came through the mirror. Imaginary light rays extended behind mirrors are called sight lines. J.M. Gabrielse
    13. 13. Plane Mirrors (flat mirrors) object image How do we see images in mirrors? Light reflected off the mirror converges to form an image in the eye. The eye perceives light rays as if they came through the mirror. Imaginary light rays extended behind mirrors are called sight lines. The image is virtual since it is formed by imaginary sight lines, not real light rays. J.M. Gabrielse
    14. 14. Spherical Mirrors (concave & convex) J.M. Gabrielse
    15. 15. Concave & Convex (just a part of a sphere) • C r • F f C: the center point of the sphere r: radius of curvature (just the radius of the sphere) F: the focal point of the mirror (halfway between C and the mirror) f: the focal distance, f = r/2 J.M. Gabrielse
    16. 16. Concave Mirrors (caved in) • F optical axis Light rays that come in parallel to the optical axis reflect through the focal point. J.M. Gabrielse
    17. 17. Concave Mirror (example) • F optical axis J.M. Gabrielse
    18. 18. Concave Mirror (example) • F optical axis The first ray comes in parallel to the optical axis and reflects through the focal point. J.M. Gabrielse
    19. 19. Concave Mirror (example) • F optical axis The first ray comes in parallel to the optical axis and reflects through the focal point. The second ray comes through the focal point and reflects parallel to the optical axis. J.M. Gabrielse
    20. 20. Concave Mirror (example) • F optical axis The first ray comes in parallel to the optical axis and reflects through the focal point. The second ray comes through the focal point and reflects parallel to the optical axis. A real image forms where the light rays converge. J.M. Gabrielse
    21. 21. Concave Mirror (example 2) • F optical axis J.M. Gabrielse
    22. 22. Concave Mirror (example 2) • F optical axis The first ray comes in parallel to the optical axis and reflects through the focal point. J.M. Gabrielse
    23. 23. Concave Mirror (example 2) • F optical axis The first ray comes in parallel to the optical axis and reflects through the focal point. The second ray comes through the focal point and reflects parallel to the optical axis. J.M. Gabrielse
    24. 24. Concave Mirror (example 2) • F optical axis The first ray comes in parallel to the optical axis and reflects through the focal point. The second ray comes through the focal point and reflects parallel to the optical axis. The image forms where the rays converge. But they don’t seem to converge. J.M. Gabrielse
    25. 25. Concave Mirror (example 2) • F optical axis The first ray comes in parallel to the optical axis and reflects through the focal point. The second ray comes through the focal point and reflects parallel to the optical axis. A virtual image forms where the sight rays converge. J.M. Gabrielse
    26. 26. Your Turn (Concave Mirror) object • F optical axis concave mirror • Note: mirrors are thin enough that you just draw a line to represent the mirror • Locate the image of the arrow J.M. Gabrielse
    27. 27. Your Turn (Concave Mirror) object • F optical axis concave mirror • Note: mirrors are thin enough that you just draw a line to represent the mirror • Locate the image of the arrow J.M. Gabrielse
    28. 28. Convex Mirrors (curved out) • F optical axis Light rays that come in parallel to the optical axis reflect from the focal point. The focal point is considered virtual since sight lines, not light rays, go through it. J.M. Gabrielse
    29. 29. Convex Mirror (example) • F optical axis J.M. Gabrielse
    30. 30. Convex Mirror (example) • F optical axis The first ray comes in parallel to the optical axis and reflects through the focal point. J.M. Gabrielse
    31. 31. Convex Mirror (example) • F optical axis The first ray comes in parallel to the optical axis and reflects through the focal point. The second ray comes through the focal point and reflects parallel to the optical axis. J.M. Gabrielse
    32. 32. Convex Mirror (example) • F optical axis The first ray comes in parallel to the optical axis and reflects through the focal point. The second ray comes through the focal point and reflects parallel to the optical axis. The light rays don’t converge, but the sight lines do. J.M. Gabrielse
    33. 33. Convex Mirror (example) • F optical axis The first ray comes in parallel to the optical axis and reflects through the focal point. The second ray comes through the focal point and reflects parallel to the optical axis. The light rays don’t converge, but the sight lines do. A virtual image forms where the sight lines converge. J.M. Gabrielse
    34. 34. Your Turn (Convex Mirror) • F object optical axis convex mirror • Note: mirrors are thin enough that you just draw a line to represent the mirror • Locate the image of the arrow J.M. Gabrielse
    35. 35. Your Turn (Convex Mirror) object image • F optical axis convex mirror • Note: mirrors are thin enough that you just draw a line to represent the mirror • Locate the image of the arrow J.M. Gabrielse
    36. 36. Lensmaker’s Equation 1 1 1 = + f di do ƒ = focal length do = object distance di = image distance if distance is negative the image is behind the mirror J.M. Gabrielse
    37. 37. Magnification Equation hi − di m= = ho do m = magnification hi = image height ho = object height If height is negative the image is upside down if the magnification is negative the image is inverted (upside down) J.M. Gabrielse
    38. 38. Refraction (bending light) Refraction is when light bends as it passes from one medium into another. normal air θi When light traveling through air passes into the glass block it is refracted towards the normal. glass block θr When light passes back out of the glass into the air, it is refracted away from the normal. Since light refracts when it changes mediums it can be aimed. Lenses are shaped so light is aimed at a focal point. θi θr normal air J.M. Gabrielse
    39. 39. Lenses The first telescope, designed and built by Galileo, used lenses to focus light from faraway objects, into Galileo’s eye. His telescope consisted of a concave lens and a convex lens. light from object convex lens concave lens Light rays are always refracted (bent) towards the thickest part of the lens. J.M. Gabrielse
    40. 40. Concave Lenses Concave lenses are thin in the middle and make light rays diverge (spread out). • F optical axis If the rays of light are traced back (dotted sight lines), they all intersect at the focal point (F) behind the lens. J.M. Gabrielse
    41. 41. Concave Lenses • F optical axis Light rays that come in parallel to the opticalignore the thickness offocallens. The light rays behave the same way if we axis diverge from the the point. J.M. Gabrielse
    42. 42. Concave Lenses • F optical axis Light rays that come in parallel to the optical axis still diverge from the focal point. J.M. Gabrielse
    43. 43. Concave Lens (example) • F optical axis The first ray comes in parallel to the optical axis and refracts from the focal point. J.M. Gabrielse
    44. 44. Concave Lens (example) • F optical axis The first ray comes in parallel to the optical axis and refracts from the focal point. The second ray goes straight through the center of the lens. J.M. Gabrielse
    45. 45. Concave Lens (example) • F optical axis The first ray comes in parallel to the optical axis and refracts from the focal point. The second ray goes straight through the center of the lens. The light rays don’t converge, but the sight lines do. J.M. Gabrielse
    46. 46. Concave Lens (example) • F optical axis The first ray comes in parallel to the optical axis and refracts from the focal point. The second ray goes straight through the center of the lens. The light rays don’t converge, but the sight lines do. A virtual image forms where the sight lines converge. J.M. Gabrielse
    47. 47. Your Turn (Concave Lens) object • F optical axis concave lens • Note: lenses are thin enough that you just draw a line to represent the lens. • Locate the image of the arrow. J.M. Gabrielse
    48. 48. Your Turn (Concave Lens) object • Fimage optical axis concave lens • Note: lenses are thin enough that you just draw a line to represent the lens. • Locate the image of the arrow. J.M. Gabrielse
    49. 49. Convex Lenses Convex lenses are thicker in the middle and focus light rays to a focal point in front of the lens. The focal length of the lens is the distance between the center of the lens and the point where the light rays are focused. J.M. Gabrielse
    50. 50. Convex Lenses • F optical axis J.M. Gabrielse
    51. 51. Convex Lenses • F optical axis Light rays that come in parallel to the optical axis converge at the focal point. J.M. Gabrielse
    52. 52. Convex Lens (example) • F optical axis The first ray comes in parallel to the optical axis and refracts through the focal point. J.M. Gabrielse
    53. 53. Convex Lens (example) • F optical axis The first ray comes in parallel to the optical axis and refracts through the focal point. The second ray goes straight through the center of the lens. J.M. Gabrielse
    54. 54. Convex Lens (example) • F optical axis The first ray comes in parallel to the optical axis and refracts through the focal point. The second ray goes straight through the center of the lens. The light rays don’t converge, but the sight lines do. J.M. Gabrielse
    55. 55. Convex Lens (example) • F optical axis The first ray comes in parallel to the optical axis and refracts through the focal point. The second ray goes straight through the center of the lens. The light rays don’t converge, but the sight lines do. A virtual image forms where the sight lines converge. J.M. Gabrielse
    56. 56. Your Turn (Convex Lens) • F object optical axis image convex lens • Note: lenses are thin enough that you just draw a line to represent the lens. • Locate the image of the arrow. J.M. Gabrielse
    57. 57. Your Turn (Convex Lens) • F object optical axis image convex lens • Note: lenses are thin enough that you just draw a line to represent the lens. • Locate the image of the arrow. J.M. Gabrielse
    58. 58. Thanks/Further Info • Faulkes Telescope Project: Light & Optics by Sarah Roberts • Fundamentals of Optics: An Introduction for Beginners by Jenny Reinhard • PHET Geometric Optics (Flash Simulator) • Thin Lens & Mirror (Java Simulator) by Fu-Kwun Hwang J.M. Gabrielse
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