Resource Lesson
Refraction of Light
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Refraction
means the bending of a wave resulting from a change in its velocity as its moves from one medium to another. Since the frequency of a wave cannot change, independent of the source changing its frequency when it originally emits a wave, this change in wave velocity must result from a change in its wavelength in the second medium.
As shown in the above diagram, when the waves encounter an oblique interface, both their direction and wavelength change. In the instance illustrated, the wavelengths shorten and the refracted rays "bend towards the normal" as the waves enter the shallow, or slower, medium: θ
_{r}
< θ
_{i}
.
This diagram illustrates that when an incident wave crosses an interface and its wavefronts are parallel to the interface, the wave will still exhibit a change in wavelength but there will be no change in direction since its rays are parallel to the normals.
Now we will extend our discussion of refraction to light waves. To quantify the degree of refraction, we will introduce a dimensionless quantity called the
index of refraction
,
n
.
n = c/v
In this formula,
c
is the speed of alight in a vacuum, 3 x 10
^{8}
m/sec
v
represents the average speed of light in the optically dense medium
n
is the medium's index of refraction
This defining formula can be easily modified to describe the changes that occur in wavelength during refraction.
n = c/v
n = (f λ)/(f λ
_{n}
)
n = λ/λ
_{n}
Notice that the frequency,
f
, cancels since it is an invariant and does not depend on the medium through which the wave is traveling.
Some common indices of refraction for a midrange wavelength of light (589 nm, a prominent line in the
emission spectrum of sodium
) are:
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
Refer to the following information for the next two questions.
From the table shown above, crown glass has an index of refraction equal to 1.52.
What is the average speed of 589 nm light through this type of glass?
What is its new wavelength while traveling through the crown glass?
Refer to the following information for the next question.
A slab of crown glass is 15 mm thick and rays of 528 nm light strike its top surface perpendicularly.
How long will it take the light to travel through the slab?
Unless otherwise specified, when working general problems we will use the following three common indices for any frequency of visible light:
air, n = 1.00
water, n = 1.33
generic glass, n = 1.5
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