Download Refraction - Kelso High School

Refraction
Radiation & Matter 3:
Refraction
AIM
The effects of refraction (the change of direction that takes place when light passes from air
into glass) may have been met during an earlier study of Physics.
The aim of this unit is to derive a relationship between the angle of incidence and the angle of
refraction when light passes from one medium into another, and to consider how the amount
of bending depends on the frequency (colour) of the light.
The ability to measure and know the bending power or materials is particularly important to
lens makers and optical instrument designers.
OBJECTIVES
At the end of this unit you should be able to:
•
state that the ratio
sin θ 1
is a constant when light passes obliquely from medium 1
sin θ 2
to medium 2.
•
state that the absolute refractive index n of a medium is the ratio
sin θ 1
where θ1 is
sin θ 2
in a vacuum (or air as an approximation) and θ2 is in the medium.
•
carry out calculations using this relationship.
•
describe the principles of a method for measuring the absolute refractive index of
glass for monochromatic light.
•
state that the refractive index depends on the frequency of the incident light.
•
state that the frequency of a wave is unaltered by a change in medium.
•
state and use the relationships for refraction of a wave from medium 1 to medium 2:
n=
Strathaven Academy
sin θ 1
v1
λ1
=
=
sin θ 2
v2
λ2
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Radiation and Matter
Refraction
Activity 5
Refractive index
Aim:
To find how changing the incident angle affects the refracted angle when light enters a
Perspex block.
Apparatus:
RayZer light box set to give 1 ray
9V power supply
semicircular Perspex block
ruler
protractor
C
Normal
θ1
B
θ2
A
Initial set up:
• Place the block on a sheet of white paper and trace its outline.
• Using the ruler and protractor, draw the normal at the midpoint of the straight edge
(B).
Obtaining results:
•
Draw in the line AB, making the angle θ1 equal to 10 degrees.
•
Put the block on the paper. Shine a ray of light along line AB and mark the direction
of the refracted ray.
•
Remove the block and draw in the line BC.
•
Measure the angle θ2.
• Repeat these steps for other values of the incident angle.
sin θ 1
• Calculate sin θ1 and sin θ2 for each row, and the ratio
sin θ 2
• Draw a graph of sin θ1 vs sin θ2.
θ1 (°)
θ2 (°)
sin θ1
sin θ2
.
sin θ 1
sin θ 2
10
20
30
40
50
60
70
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Radiation and Matter
Refraction
REFRACTION OF LIGHT
Refractive index
By varying the angle θa, a relationship between θa
and θg can be found.
sin θ a
Experiment shows that
is constant.
sin θ g
This constant is called the reflective index n of
the medium.
sin θ a
=n
sin θ g
The values given in data books are called absolute refractive indices. These are the ratios of
the sine of the angle in a vacuum, not air, to the sine of the angle in the medium. However,
for most practical purposes we can use air.
sin θ a
=n
sin θ m
θa = angle in air measured relative to normal
θm = angle in medium measured relative to normal.
The refractive index measures the effect a medium has on light. The greater the refractive
index, the greater the change in speed and direction.
The refractive index of a medium is the same whether light moves from air into the medium
or vice versa.
The absolute refractive index is always a value greater than (or equal to) 1.
Example
Using information from the diagram, find the refractive index of the clear plastic.
All angles must be measured from the normal.
θa = 90 – 30 = 60°
n=
θm = 90 – 54 = 36°
sin θ a
sin 60
=
= 1.47
sin θ m
sin 36
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Radiation and Matter
Refraction
Refractive index and frequency of light
The refractive index of a medium depends upon the frequency (colour) of the incident light.
When light enters a glass prism, it separates into its component colours and produces a
spectrum. This happens because each colour (frequency) is refracted by a different amount.
Since violet is refracted more than red (i.e. it has changed speed and direction by a greater
amount), it follows that the refractive index for violet light must be greater than the refractive
index for red light.
Refractive index and relationship with v, λ and θ
n=
sin θ a
va
λa
=
=
sin θ m
vm
λm
In general, from medium 1 to medium 2:
sin θ 1
v1
λ1
=
=
sin θ 2
v2
λ2
Example
Calculate the speed of light in glass of refractive index 1.50.
va
va
3 × 108
v m = 2 × 108 m s-1
=n
= 1.50
= 1.50
vm
vm
vm
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Radiation and Matter
Refraction
Refraction of light
18. Calculate the refractive index n of each of the materials below:
19. Calculate the missing angle in each of the following diagrams:
20. The refractive index of the material shown in the diagram below is 1.35.
a) Calculate the angle r.
b) Find the velocity of the light in the material.
21. A ray of light of wavelength 6.00 × 10-7 m passes from air to glass as shown below.
a)
b)
c)
d)
e)
Calculate the refractive index of the glass.
Calculate the speed of light in the glass.
Calculate the wavelength of the light in the glass.
Calculate the frequency of the light in air.
State the frequency of the light in the glass.
Strathaven Academy
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Radiation and Matter
Refraction
22. A ray of light of wavelength 500 nm passes from air into perspex of refractive index 1.50
as shown.
a) Calculate the angle r.
b) Calculate the speed of light in the perspex.
c) Calculate the wavelength of light in perspex.
23. The refractive index for red light in crown glass is 1.513 and for violet light it is 1.532.
a) Using this information, explain why white light can produce a spectrum when passed
through crown glass.
A ray of white light passes through a semi-circular block of crown glass as shown and
produces a spectrum.
b) Which exit ray is red and which ray is violet?
c) Calculate the refracted angle in air for each of the exit rays.
d) Find angle x, the angle between the red and violet rays.
24. A ray of white light is dispersed by a prism producing a spectrum, S.
The angle x° is found to be 0.7°.
If the refractive index for red light is 1.51, calculate the refractive index for blue light.
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Radiation and Matter