and Refraction Lenses
AP Physics B
Refraction
Refraction is based on the idea that LIGHT is passing through one MEDIUM into another. The question is, WHAT HAPPENS?
Suppose you are running on the beach with a certain velocity when you suddenly need to run into the water. What happens to your velocity? IT CHANGES! Refraction Fact #1: As light goes from one medium to another, the velocity CHANGES!
Suppose light comes from air, which in this case will be considered to be a vacuum, strikes a boundary at some angle of incidence measured from a normal line ,and goes into water.
The ratio of the two speeds can be compared.
Refraction
The denominator in this case will ALWAYS be smaller and produce a unitless value greater or equal to 1. This value is called the new medium's INDEX OF REFRACTION, n.
All substances have an index of refraction and can be used to identify the material.
Refraction
Suppose you decide to go spear fishing, but unfortunately you aren't having much luck catching any fish.
The cause of this is due to the fact that light BENDS when it reaches a new medium. The object is NOT directly in a straight line path, but rather it's image appears that way. The actual object is on either side of the image you are viewing.
Refraction Fact #2: As light goes from one medium to another, the path CHANGES!
What EXACTLY is light doing when it reaches a new medium? We don't want you to think ALL of the light refracts.
Some of the light REFLECTS off the boundary and some of the light REFRACTS through the boundary. Angle of incidence = Angle of Reflection Angle of Incidence > or < the Angle of refraction depending on the direction of the light
Refraction
Refraction Going from Air to The index of refraction, n, for air Water (vacumm) is equal to 1. The index of
refraction for water is 1.33. If you are going from a LOW "n" to a HIGH "n", your speed DECREASES and the angle BENDS TOWARDS the normal
Refraction Going from Water into Air
The index of refraction, n, for air (vacumm) is equal to 1. The index of refraction for water is 1.33. If are you going from a HIGH "n" to a LOW "n", your speed INCREASES and the angle BENDS AWAY the normal Note: If the angles are EQUAL, then the "n" must be equal for each. The ray will pass straight through.
Refraction Snell's Law
A scientist by the name of Snell discovered that the ratios of the index's and the ratio of the sine of the angles are the same value!
n1 sin 2 = n2 sin 1
Snell ' s Law n1 sin 1 = n2 Sin 2
Example
The refractive index of the gemstone, Aquamarine, is 1.577. Suppose a ray of light strikes a horizontal boundary of the gemstone with an angle of incidence of 23 degrees from air.
Calculate the SPEED of light in Aquamarine
c c 3x108 n= vm = = vm n 1.577 vm = 1.90 x 10
8
m/s
Calculate the angle of refraction within Aquamarine
n1 sin 1 = n2 sin 2
-1
(1)(sin 23) = 1.577 sin 2 sin 23 = sin ( )= 1.577
14.34 degrees
Total Internal Reflection
There is a special type of refraction that can occur ONLY when traveling from a HIGH "n" medium to a LOW "n" medium.
Suppose we are traveling FROM water and going into air. Should the ANGLE OF INCIDENCE get TOO LARGE, the angle of refraction will EQUAL 90 DEGREES. We call this special angle of incidence the CRITICAL ANGLE, c, for that material (water in this case)
Total Internal Reflection
If we EXCEED the critical angle, for that material, the ray will reflect INTERNALLY within the material. We call this idea TOTAL INTERNAL REFLECTION.
In this figure, the angle of incidence EXCEEDS the critical angle for water and the ray reflects according to the law of reflection at the boundary.
So the question is , how can you calculate the critical angle? Remember, it is when the refracted ray is equal to 90 degrees
The Critical Angle
n1 sin c = n2 sin 2 , Sin90 = 1 sin c = n2 n1
c
Example
Suppose a light ray is traveling in heavy flint glass( n = 1.65) and once it strikes the boundary, enters air. Calculate the critical angle for flint glass.
n1 sin c = n2 sin 2 , Sin90 = 1
n2 sin c = n1 1 1 -1 sin c = c = sin ( ) 1.65 1.65 c = 37.3 degrees