Objectives
Total Internal Reflection
Review of Snell’s Law
Normal
Incident Ray
Angle of Incidence
Normal
Angle of Refraction
Refracted Ray
Medium 1 (n1)
Surface (interface)
Medium 2 (n2)
n1·sinθ1 = n2·sinθ2
Snell’s Law Works in the
Other Direction
Reflected Ray
θ1
Snell’s Law:
• Measure indices of refraction for different
media
• Describe the conditions under which total
internal reflection occurs and determine the
critical angle
• Explain and solve problems involving total
internal reflection and critical angle
• Explain, using a diagram, total internal
reflection in an optical device
• Analyze situations involving total internal
reflections
θ1
Medium 1 (n1)
Surface (interface)
Medium 2 (n2)
θ2
Angle of
refraction
Reflected Ray
θ2
Refracted Ray
Incident Ray
Angle of
incidence
What if θi = 0°?
And if it increases?
Air, na = 1
θ r = 0°
θi = 0°
Water, nw = 1.33
And if it increases?
Air, na = 1
Θr = 42°
Θi = 30°
Water, nw = 1.33
Air, na = 1
Θr = 13°
Θi = 10°
Water, nw = 1.33
And if it increases?
Air, na = 1
Θr = 59°
Θi = 40°
Water, nw = 1.33
And if it increases?
Air, na = 1
Θr = 77°
Θi = 47°
Water, nw = 1.33
And if it increases?
Air, na = 1
And if it increases?
Air, na = 1
Θr = 85°
Θi = 48°
Water, nw = 1.33
And if it increases?
Air, na = 1
Total Internal Reflection
Θr = 90°
Θi = 48°
Water, nw = 1.33
Θr = ERROR
Θi = 48.7536°
Water, nw = 1.33
Critical Angle
Critical Angle
• Where did 48.7535° come from?
Air, na = 1
• Where did 48.7535° come from?
ni sin θ i = nr sin θ r
at critical angle θ r = 90°
Θr = 0°
Θi = 48.7535°
Water, nw = 1.33
but sin 90° = 1
also sin θ i = critical angle
therefore
ni sin θ crit = 1 ∗ nr
θ crit
Poor fish can only see a little circle!
•The fish can only see a circle of sky!
•The circle is determined based on the θCRIT of water (49°)
•Beyond 49° fishy only sees the reflection of surroundings
na = 1
Θr=0°
n
= sin −1  r 
 ni 
Can we use this effect?
Yes! It is the basis of fibre optics.
Θi=48.7°
nw = 1.33
Fibre Optics
Homework
Heath: p.482 #9, 13, 30, 32, 34, 36
Summary
• sinθ1/sinθ2 is constant in a given medium
• Incident & Refracted rays are on opposite
sides of the normal
• When light goes into a denser medium it
bends towards the normal
• When light goes into a less dense medium
it bends away from the normal
• Light doesn’t refract when it enters at 90°
• θCRIT = arcsin(n2/n1) = sin-1(n2/n1)
• Total internal reflection occurs if:
n1>n2
and if
θ1>θCRIT
• When θ1=θCRIT then θ2=90°