Resource Lesson
Snell's Law
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To determine the degree to which a light ray bends as it obliquely transitions from one medium to another, we will use our knowledge of refraction and Snell's Law. For those interested in seeing a derivation of Snell's Law, please reference this
accompanying lesson
.
n
_{1}
sin θ
_{1}
= n
_{2}
sin θ
_{2}
where
n
_{1}
is the
index of refraction
for the first medium
n
_{2}
is the index of refraction for the second medium
that angles θ
_{1}
and θ
_{2}
are always measured from the normal, NEVER from the interface.
Here is a list of common indices for the 589 nm wavelength in
sodium's spectrum
.
medium
index
medium
index
vacuum
1.00000
fused quartz
1.46
air (STP)
1.00029
crown glass
1.52
water (20ºC)
1.33
polystyrene
1.55
acetone
1.36
carbon disulfide
1.63
ethyl alcohol
1.36
flint glass (heavy)
1.65
sugar solution (30%)
1.38
sapphire
1.77
sugar solution (80%)
1.49
diamond
2.42
If n
_{2}
> n
_{1}
, then the light is entering an optically more dense medium and the ray will bend "towards the normal" as it enters n
_{2}
.
This phenomena occurs because the
wavelength shortens in the second medium
resulting in the light having a slower average velocity.
Note that the ray bends towards the normal as the light enters the glass and that θ
_{glass}
is smaller than θ
_{air}
.
If n
_{2}
< n
_{1}
, then the light is entering an optically less dense medium and the ray bends "away from the normal" when it enters n
_{2}
.
This phenomena occurs because the wavelength lengthens in the second medium resulting in the light having a faster average velocity.
Note that the ray bends away from the normal as the light exits the glass as it returns into the air and that θ
_{air}
is greater than θ
_{glass}
.
Refer to the following information for the next question.
If a ray of light strikes the top surface of a dish of water at an angle of 37º to the vertical, at what angle will it be refracted as it enters the water?
Refer to the following information for the next six questions.
Suppose a ray of light enters a glass slab (n = 1.56) that is covered with water (n = 1.33) as shown in the diagram below. Each layer is 10 mm thick and the initial angle of incidence equals 30º. Our goal in the following series of questions is to determine the beam's linear displacement, X, from its initial straight-line path when it emerges from the bottom of the glass.
At what angle does the ray enter the water?
What is the value for x
_{1}
in the diagram shown in the hint?
At what angle does the ray enter the glass?
What is the value for x
_{2}
in the diagram shown in the hint?
What is the value for x
_{3}
in the diagram shown in the hint?
What is the value for X?
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