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Useful reference for dead time could be used to improve the article.
Physics and radiobiology of nuclear medicine
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Addition of paralysable/non-paralysable system graph
Graphic display of the effect of the two types of counting systems, showing dead time loss
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At a particular angle of incidence,
θ
B
{\displaystyle \theta _{\mathrm {B} }}
(also known as Brewster's angle), the reflectivity,
r
∥
→
0
{\displaystyle r_{\parallel }\to 0}
. From the Fresnel equation for the reflectivity of a wave with an electric field polarized parallel to the plane of incidence;
r
∥
=
n
1
cos
θ
T
−
n
2
cos
θ
B
n
1
cos
θ
T
+
n
2
cos
θ
B
=
0
{\displaystyle r_{\parallel }={\frac {n_{1}\cos \theta _{\mathrm {T} }-n_{2}\cos \theta _{\mathrm {B} }}{n_{1}\cos \theta _{\mathrm {T} }+n_{2}\cos \theta _{\mathrm {B} }}}=0}
where
θ
T
{\displaystyle \theta _{\mathrm {T} }}
is the angle of transmission.
From this;
n
1
cos
θ
T
=
n
2
cos
θ
B
{\displaystyle n_{1}\cos \theta _{\mathrm {T} }=n_{2}\cos \theta _{\mathrm {B} }}
Using simple geometry, the condition that the refracted light is perpendicular to the reflected light can be expressed as;
θ
B
+
θ
T
=
90
∘
{\displaystyle \theta _{\mathrm {B} }+\theta _{\mathrm {T} }=90^{\circ }}
We then obtain;
n
1
cos
(
π
2
−
θ
B
)
=
n
1
sin
θ
B
=
n
2
cos
θ
B
{\displaystyle n_{1}\cos \left({\frac {\pi }{2}}-\theta _{\mathrm {B} }\right)=n_{1}\sin \theta _{\mathrm {B} }=n_{2}\cos \theta _{\mathrm {B} }}
Using trigonometric identities, this rearranges to;
sin
θ
B
cos
θ
B
=
tan
θ
B
=
n
2
n
1
{\displaystyle {\frac {\sin \theta _{\mathrm {B} }}{\cos \theta _{\mathrm {B} }}}=\tan \theta _{\mathrm {B} }={\frac {n_{2}}{n_{1}}}}
Incorporate alternative version of ideal gas equation:
P
=
ρ
R
T
μ
{\displaystyle P={\frac {\rho RT}{\mu }}}