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Theory – PASCO OS-8542 BLACK BODY LIGHT SOURCE User Manual

Page 6

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Black Body Instruction Manual

012-07105B

2

GAIN

10

100

1

The 60-degree prism is mounted so that the
back face is perpendicular to the incoming
light, as shown in Figure 1. A schematic of
the prism and the path of light is shown in
Figure 2 below. Since the prism angle is 60
degrees, it can be shown that

(1)

θ

2

+

θ

3

= 60

°

And using Snell’s law at each interface,

(2) sin (60

°) = n sin (θ

2

) and

(3) sin (

θ) = n sin(θ

3

)

Combining equations (3) and (1) yields

(4) sin (

θ) = n sin (60° – θ

2

)

which, using the double angle formula
becomes

(5) sin (

θ) = n{ sin (60°) cos (θ

2

) – sin (

θ

2

) cos (60

°)}

Figure 1: Path of Light Through the Prism
Spectrophotometer

Theory

black body light

collimating slits

collimating lens

light sensor

aperture slits

prism mount
with prism

direction of light

Now use a trig identity to change from cos to sin, and (5) becomes

(6) sin

θ = n sin 60° 1 – sin

2

θ

2

1
2

– n sin

θ

2

cos 60

°

= sin 60° n

2

– n

2

sin

2

θ

2

1
2

– n sin

θ

2

cos 60

°

If we now use (2), equation 6 becomes

(7) sin(

θ) = sin(60°)[n

2

– sin

2

(60

°)]

1
2

– sin(60

°)cos(60°)

Solving (7) for n gives

(8) n =

sin

θ

sin60

+ cos60

2

+ sin

2

60

And finally, if we simplify,

The Cauchy equation gives the relationship between the
wavelength and the index of refraction.

(10) n(

λ) =

A

λ

2

+ B

where A and B depend on the type of glass.

Figure 2: Schematic of a Prism

n

path of light

θ

2

θ

θ

3

60°

60°