1. 17.1 Reflection and Refraction
Key Question:
How do we describe the reflection and refraction of light?

2. 17.1 Reflection and Refraction
The overall study of how light behaves is called optics.
The branch of optics that focuses on the creation of images is called geometric optics, because it is based on relationships between angles and lines that describe light rays.

3. 17.1 Reflection and Refraction
A lens is an optical device that is used to bend light in a specific way.
A converging lens bends light so that the light rays come together to a point.
A diverging lens bends light so it spreads light apart instead of coming together.

4. 17.1 Reflection and Refraction
Mirrors reflect light and allow us to see ourselves.
A prism is another optical device that can cause light to change directions.
A prism is a solid piece of glass with flat polished surfaces.

5. 17.1 Reflection
Images appear in mirrors because of how light is reflected by mirrors.
The incident ray follows the light falling onto the mirror.
The reflected ray follows the light bouncing off the mirror.

6. 17.1 Reflection
In specular reflection each incident ray bounces off in a single direction.
A surface that is not shiny creates diffuse reflection.
In diffuse reflection, a single ray of light scatters into many directions.

7. Law of Reflection The incident ray strikes the mirror.
The reflected ray bounces off.
The angle of incidence equals the angle of reflection.

8. 17.1 Law of reflection
30o
30o
1) You are asked for a ray diagram and the angle of reflection.
2) You are given the angle of incidence.
3) The law of reflection states the angle of reflection equals the angle of incidence.
4) The angle of reflection is 30°.
A light ray is incident on a plane mirror with a 30 degree angle of incidence.
Sketch the incident and reflected rays and determine the angle of reflection.

9. 17.1 Refraction
Light rays may bend as they cross a boundary from one material to another, like from air to water.
This bending of light rays is known as refraction.
The light rays from the straw are refracted (or bent) when they cross from water back into air before reaching your eyes.

10. 17.1 Refraction
When a ray of light crosses from one material to another, the amount it bends depends on the difference in index of refraction between the two materials.

11. 17.1 Index of refraction
The ability of a material to bend rays of light is described by the index of refraction (n).

13. 17.1 Snell's law of refraction
Snell’s law is the relationship between the angles of incidence and refraction and the index of refraction of both materials.
Angle of refraction
(degrees)
Angle of incidence
(degrees)
ni sin Qi = nr sin Qr
Index of refraction of incident material
Index of refraction of refractive material

14. 17.1 Calculate the angle of refraction
A ray of light traveling through air is incident on a smooth surface of water at an angle of 30° to the normal.
Calculate the angle of refraction for the ray as it enters the water.
1) You are asked for the angle of refraction.
2) You are told the ray goes from air into water at 30 degrees.
3) Snell’s law:
ni sin(θi) = nr sin(θr)
ni = 1.00 (air), nr = 1.33 (water)
4) Apply Snell’s law to find θr.
1.00sin(30°) = 1.33 sin(θr)
sin(θr) = 0.5 ÷ 1.33 = 0.376
Use the inverse sine function to find the angle that has a
sine of
θr = sin-1(0.376) = 22°

15. The angle at which light begins reflecting back into a refractive material is called
the critical angle, and it depends on the index of refraction.
The critical angle for water is about 49 degrees.

16. 17.1 Dispersion and prisms
When white light passes through a glass prism, blue is bent more than red.
Colors between blue and red are bent proportional to their position in the spectrum.

17. 17.1 Dispersion and prisms
The variation in refractive index with color is called dispersion.
A rainbow is an example of dispersion in nature.
Tiny rain droplets act as prisms separating the colors in the white light rays from the sun.

18. 17.2 Mirrors, Lenses, and Images
Key Question:
How does a lens or mirror form an image?

19. 17.2 Mirrors, Lenses, and Images
We see a world of images created on the retina of the eye by the lens in the front of the eye.

20. 17.2 Mirrors, Lenses, and Images
Objects are real physical things that give off or reflect light rays.
Images are “pictures” of objects that are formed in space where light rays meet.

21. 17.2 Mirrors, Lenses, and Images
The most common image we see every day is our own reflection in a mirror.
The image in a mirror is called a virtual image because the light rays do not actually come together.
The virtual image in a flat mirror is created by the eye and brain.

22. 17.2 Mirrors, Lenses, and Images
Light rays that enter a converging lens parallel to its axis bend to meet at a point called the focal point.
The distance from the center of the lens to the focal point is called the focal length.
The optical axis usually goes through the center of the lens.

23. A converging lens bends an incident light ray parallel to the optical axis toward the focal point.
A diverging lens bends an incident light ray parallel to the axis outward, away from the focal point

24. 17.2 The image formed by a lens
A lens can form a virtual image just as a mirror does.
Rays from the same point on an object are bent by the lens so that they appear to come from a much larger object.

25. 17.2 The image formed by a lens
A converging lens can also form a real image.
In a real image, light rays from the object actually come back together.

26. 17.2 Drawing ray diagrams
A ray diagram is the best way to understand what type of image is formed by a lens, and whether the image is magnified or inverted.
These three rays follow the rules for how light rays are bent by the lens:
A light ray passing through the center of the lens is not deflected at all (A).
A light ray parallel to the axis passes through the far focal point (B).
A light ray passing through the near focal point emerges parallel to the axis (C).

29. 17.3 The sharpness of an image
Defects in the image are called aberrations and can come from several sources.
Chromatic aberration is caused by dispersion, when different colors focus at different distances from the lens.

30. 17.3 Thin lens formula 1 + 1 = 1 do di df
The thin lens formula is a mathematical way to do ray diagrams with algebra instead of drawing lines on graph paper.
= 1
do di df
Object
distance
(cm)
focal
length (cm)
Image distance
(cm)

31. 17.3 Use the thin lens formula
1) You are asked for image distance.
2) You are given the focal length and object distance.
3) The thin lens formula applies:
1/di = 1/f — 1/do
4) Solve for di
1/di = 1/4 — 1/6
1/di = 3/12 — 2/12 = 1/12
di = 12 cm
The image forms 12 cm to the right of the lens.
Calculate the location of the image if the object is 6 cm in front of a converging lens with a focal length of 4 cm.

32. Mirror Ray Tracing: Limitations
As noted in the book, these ray tracing rules are an approximation. For this approximation to be accurate, the paraxial rays should be closer to the axis, and the object should be small compared to the mirror radius.
We’ve drawn these examples in an exaggerated manner, because it is easier to see.
This is still a very useful technique, though, to determine the approximate location and size of the image. C F

33. Clicker Question A B C F D
Incoming ray: B C F
axis D
Using our ray tracing rules, which is the correct reflected ray for the incoming ray parallel to the axis?
The colors are just for clarity and the letter C indicates the center of curvature, not a ray option. RAY D IS CORRECT E

34. Spherical Lenses
What if we don’t want to have to look at a reflection to magnify or reduce an image?
We can use refractive optics instead (lenses)

35. Convex Glass Surface AIR (fast) GLASS (slow) C
normal
AIR (fast)
GLASS (slow)
fast to slow bends towards the normal
axis C
A concave surface is called “converging” because parallel rays converge towards one another

36. Convex Glass Surface GLASS AIR C
normal
GLASS
AIR
slow to fast bends away from the normal
axis C
The surface is converging for both air to glass rays and glass to air rays

37. Concave Glass Surface AIR GLASS CC
axis
A concave surface is called “diverging” because parallel rays diverge away from one another

38. Concave Glass Surface GLASS AIR CC
axis
Again, the surface is diverging for both air to glass rays and glass to air rays

39. Lenses converging lens “bi-convex” has two convex surfaces
diverging lens
“bi-concave”
has two concave surfaces

40. Compare to Mirrors Convex Concave
Note that this is opposite from mirrors, for which a convex surface is diverging and a concave surface is converging. When in doubt, trace some rays!

41. Converging Lens
The focal point of a curved mirror was the image point of a distant star
It is the same for a lens
The focal point of a converging lens is where the incoming rays from a distant star all intersect.
A distant star is used to guarantee that the incoming rays are parallel
Focal distance
Focal point

42. Converging Lens F F
Note that a lens has a focal point on both sides of the lens, as compared to a mirror that only has one focal point

43. Converging Lens F
Similarly to a spherical mirror, incoming parallel rays are deflected through the focal point

44. Thin Lenses
Just as the ray tracing for mirrors is approximate and only accurate for certain situations, the ray tracing for lenses is accurate only for what are called “thin lenses”
A lens is considered “thin” if the thickness of the lens is much less than the distance from the lens to the focal point. F
thickness of lens
distance to focal point

45. Thin Lenses: Vocabulary
The distance from the focal point to the lens is called the “focal length” of the lens.
To distinguish between converging and diverging lenses, f is defined as positive for converging lenses and negative for diverging lenses. We’ll come back to this.
Focal length (f) F F

46. Converging Lens: Ray Tracing RulesF F
Another simplification that we can make is that we can draw the rays as deflecting from the center line of the lens, rather than drawing deflections at both lens surfaces. Again, this is only a good approximation for thin lenses.

47. Converging Lens: Ray Tracing RulesF F
Rule 1:
Similarly to a spherical mirror, incoming parallel rays are deflected through the focal point.

48. Converging Lens: Ray Tracing RulesF F
Rule 2:
Rays passing through the center of the lens are undeflected, they continue straight through without being bent. Several rays are shown here as examples.

49. Clicker Question
AIR
GLASS
The center of a lens is approximately flat, I’ve drawn the normal to the surface for you. Given what we know about refraction, what does this ray REALLY do when it enters the glass?
Bend up
Bend down
Go straight through

50. Converging Lens: Ray Tracing RulesF F
Rule 3:
The reverse of Rule 1, rays passing through the focal point are deflected to exit parallel to the axis

51. Converging Lens: Image Formation
The image is real and inverted. In this case, the image is about the same size as the object, but the size of the image will depend on the position of the object relative to the focal point of the lens.
Make sure you do the ray tracing to figure out the image position and size!

52. Converging Lens: Image Formation
The image is still real and inverted. We’ve moved the object closer to the lens, and the image is now magnified (larger than the object).

53. Converging Lens: Image Formation
this distance is increasing
If we move the object very close to the lens (less than the focal length) the rays passing through the lens are diverging; they will never intersect on the far side of the lens.

54. Converging Lens: Image Formation
Is this image
Real
Virtual
Recall that a virtual image means no light rays reach the image location. This configuration is what occurs when you use a magnifying glass.

55. Diverging Lens F F
With a diverging lens, parallel rays are deflected such that when extended backwards, they appear to be coming from the focal point on the other side.

56. Diverging Lens: Ray TracingF F
Parallel rays are deflected so they appear to be coming from the focal point in front of the lens.

57. Diverging Lens: Ray TracingF F
Just like for converging lenses, rays that pass through the center of the lens continue undeflected (straight) through the lens.

58. Diverging Lens: Ray TracingF F
Rays that, if extended, would pass through the focal point on the other side of the lens, are deflected to be parallel to the axis.

59. Diverging Lens: Image Formation
The image is virtual, reduced, and right side up.

60. The Lens Equation
Ray tracing is useful, but kind of tedious for all these different cases, and accuracy requires very precise drawings.
We can avoid ray tracing by using the lens equation
However, this will require some algebra.

61. Focal Length Remember we defined the focal length for a lens
We also defined the sign of f. The focal length, f, is defined as positive for converging lenses and negative for diverging lenses.
Focal length (f) F F

62. Lens Equation Quantities
We also need to define some other distances.
Focal length, f
Object distance, xo
Image distance, xi
The object distance is positive for an object to the left of the lens. The image distance is positive for a (real) image on the right of the lens. These quantities are negative for the reverse situation. Be careful with this.

63. Lens Equation Quantities
Image distance, xi
Focal length, f
Object distance, xo
The image distance is negative for a (virtual) image on the left of the lens.

64. Clicker Question Which quantities are negative in this example? F
Image distance, xi F
Focal length, f
Object distance, xo
Which quantities are negative in this example?
Image distance
Focal length
Object distance
A and B
A and C