1. Reflection and Refraction of Light
Physics 102: Lecture 17
Reflection and Refraction of Light 1

2. Exam 2 results Raw mean = 87.8 / 115 (76.3%) Scaled mean = 76.3%
Raw mean improved by 10% compared to Exam 1
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3. Recall from last time…. Reflection: qi = qr Refraction:
Flat Mirror:
image equidistant behind
Spherical Mirrors:
Concave or Convex
Today q1 q2 n2 n1
Refraction:
n1 sin(q1)= n2 sin(q2)

4. Concave Mirror Principal Rays
1) Parallel to principal axis reflects through f.
2) Through f, reflects parallel to principal axis.
3) Through center. #3 #2 O #1 f c I
Image is (in this case):
Real (light rays actually cross)
Inverted (Arrow points opposite direction)
Reduced (smaller than object)
Comment that this is “weird” to have a real image. –demo 554, flower mirage
**Every other ray from object tip which hits mirror will reflect through image tip

5. Preflight 17.1 Which ray is NOT correct?
Ray through center should reflect back on self.
p.a.
15%
43%
41% 1) C f 2) 3)

6. Mirror Equation do O f c do = distance object is from mirror: I
Works for concave,
convex, or flat O f c
do = distance object is from mirror:
Positive: object in front of mirror
Negative: object behind mirror I
di = distance image is from mirror:
Positive: real image (in front of mirror)
Negative: virtual image (behind mirror) di
Note: also works for flat mirrors (f is infinite)
f = focal length mirror:
Positive: concave mirror +R/2
Negative: convex mirror –R/2

7. Preflight 17.3
The image produced by a concave mirror of a real object is:
46%
16%
38%
Always Real
Always Virtual
Sometimes Real, Sometimes Virtual
Concave mirror: f > 0
Real Object means in front of mirror: do > 0
Mirror Equation: 
di is positive if d0 > f; negative is d0 < f.

8. ACT: Concave Mirror
Where in front of a concave mirror should you place an object so that the image is virtual?
Mirror Equation:
Close to mirror
Far from mirror
Either close or far
Not Possible
Demo: 1131; large concave mirror
Concave mirror: f > 0
Object in front of mirror: do > 0
Virtual image means behind mirror: di < 0
When do < f then di < 0 virtual image.

9. 3 Cases for Concave Mirrors
Object
Image
Virtual
Inside F C F
Object
Image
Real
Between C&F C F
Object
Image
Real
Past C

10. Magnification Equationdo O do ho
Angle of incidence
ho = height of object:
Positive: always q di
-hi
Angle of reflection I
hi = height of image:
Positive: image is upright
Negative: image is inverted
m = magnification:
Positive / Negative: same as for hi
< 1: image is reduced
> 1: image is enlarged di
Flat mirrors: m=+1

11. Solving Equations Preflight 17.2 Example
A candle is placed 6 cm in front of a concave mirror with focal length f=2 cm. Determine the image location.
di = + 3 cm (in front of mirror)
Real Image!
Preflight 17.2
Compared to the candle, the image will be:
Larger
Smaller
Same Size
p.a. C f
25%
66% 9%

12. ACT: Magnification
A 4 inch arrow pointing down is placed in front of a mirror that creates an image with a magnification of –2.
What is the size of the image?
2 inches
4 inches
8 inches
4 inches
Magnitude gives us size.
What direction will the image arrow point?
Up 2) Down
(-) sign tells us it’s inverted from object

13. 3 Cases for Concave Mirrors
Object
Image
Upright
Enlarged
Virtual
Inside F C F
Object
Image
Inverted
Enlarged
Real
Between C&F C F
Object
Image
Inverted
Reduced
Real
Past C

14. Demo: optical illusionf
image
object
Demo 296: penny mirage
Demo:
two identical spherical mirrors
each mirror is positioned at the focal point of the other

15. Convex Mirror Rays 1) Parallel to principal axis reflects through f.
2) Through f, reflects parallel to principal axis.
3) Through center. #1 O #2 #3 I f c
Make this mirror almost flat so that it is like your review mirror
Image is:
Virtual (light rays don’t really cross)
Upright (same direction as object)
Reduced (smaller than object)
(always true for convex mirrors!):

16. Solving Equations Example
A candle is placed 6 cm in front of a convex mirror with focal length f=-3 cm. Determine the image location.
Determine the magnification of the candle.
If the candle is 9 cm tall, how tall does the image candle appear to be?
di = - 2 cm (behind mirror)
Virtual Image!
m = + 1/3
hi = + 3 cm
Image is Upright!

17. Preflight 17.4
The image produced by a convex mirror of a real object is
Mirror Equation:
always real
always virtual
sometimes real and sometimes virtual
Convex mirror: f < 0
64% got this right
Object in front of mirror: do > 0
di is negative!
f is negative
do is positive
di < 0 means virtual image!
Image is always between F and mirror |di|<|f|

18. Mirror Summary Angle of incidence = Angle of Reflection Principal Rays
Parallel to P.A.: Reflects through focus
Through focus: Reflects parallel to P.A.
Through center: Reflects back on self
|f| = R/2

19. Index of Refraction v = c/n
Recall speed of light c = 3x108 m/s is in vacuum
In a medium (air, water, glass...) light is slower c l1 l2
v < c
Frequency is the same,
wavelength decreases
v = lf
vacuum
glass
n is a property of the medium:
nvacuum = 1
nair =
nwater = 1.33
nglass = 1.50
“Index of refraction”
n ≥ 1
Speed of light in medium
v = c/n
Speed of light in vacuum

20. Snell’s law of Refraction
When light travels from one medium to another, v (and l) changes (v = c/n). So the light bends!
n1 sin(q1)= n2 sin(q2)
Incident wave q1 qr q2
Reflected wave l1 n1
l2 < l1
n2 > n1
Refracted wave

21. Snell’s Law Practice Example
Usually, there is both reflection and refraction!
A ray of light traveling through the air (n=1) is incident on water (n=1.33). Part of the beam is reflected at an angle qr = 60. The other part of the beam is refracted. What is q2?
q1 = qr = 60
sin(60) = 1.33 sin(q2) 1 r
q2 = 40.6 degrees n1 n2
normal

22. Apparent Depth d d
Apparent depth: n2 n1
apparent fish
actual fish

23. See you after break!