This page contains three views of the steps in the derivation: d3js, graphviz PNG, and a table.
Notes for this derivation:
\cite{2001_HRW}; see figure 34-27 on page 824
Index | Inference Rule | Input latex | Feeds latex | Output latex | step validity | dimension check | unit check | notes |
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6 | declare identity |
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no validation is available for declarations |
8588429722:
|
8588429722:
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8 | substitute LHS of expr 1 into expr 2 |
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Nothing to split |
6831637424:
7696214507: 3061811650: |
6831637424:
7696214507: 3061811650: |
|
15 | declare final expr |
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no validation is available for declarations |
8495187962:
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8495187962:
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3 | declare initial expr |
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no validation is available for declarations |
6450985774:
|
6450985774:
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11 | declare identity |
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no validation is available for declarations |
4968680693:
|
4968680693:
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9 | divide both sides by |
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valid |
3061811650:
9756089533: |
3061811650:
9756089533: |
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5 | substitute LHS of expr 1 into expr 2 |
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Nothing to split |
1310571337:
no LHS/RHS split 2575937347: 7696214507: |
1310571337:
N/A 2575937347: 7696214507: |
|
4 | change two variables in expr |
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valid |
6450985774:
2575937347: |
6450985774:
2575937347: |
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12 | change variable X to Y |
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LHS diff is tan(pdg1464) - tan(pdg4928) RHS diff is tan(pdg1464) - tan(pdg4928) |
4968680693:
4501377629: |
4968680693:
4501377629: |
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13 | substitute LHS of expr 1 into expr 2 |
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valid |
4501377629:
2768857871: 3417126140: |
4501377629:
2768857871: 3417126140: |
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1 | declare initial expr |
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no validation is available for declarations |
8945218208:
no LHS/RHS split |
8945218208:
N/A |
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14 | apply function to both sides of expression |
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no check performed |
3417126140:
8495187962: |
3417126140:
8495187962: |
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10 | divide both sides by |
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valid |
9756089533:
2768857871: |
9756089533:
2768857871: |
|
7 | change variable X to Y |
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Nothing to split |
8588429722:
6831637424: |
8588429722:
6831637424: |
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2 | subtract X from both sides |
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Nothing to split |
8945218208:
no LHS/RHS split 1310571337: no LHS/RHS split |
8945218208:
N/A 1310571337: N/A |
symbol ID | category | latex | scope | dimension | name | value | Used in derivations | references | |
---|---|---|---|---|---|---|---|---|---|
3509 | variable |
\theta_1
\(\theta_1\) |
real | dimensionless | angle | 2 | |||
2941 | variable |
n_1
\(n_1\) |
['real'] | dimensionless | index of refraction for material 1 | 9 | |||
2243 | variable |
\theta_{\rm refracted}
\(\theta_{\rm refracted}\) |
real | dimensionless | refracted angle |
|
2 | ||
1958 | variable |
n_2
\(n_2\) |
real | dimensionless | index of refraction for material 2 | 8 | |||
7545 | variable |
\theta_2
\(\theta_2\) |
real | dimensionless | angle | 2 | |||
1464 | variable |
x
\(x\) |
['real'] | dimensionless |
|
140 | |||
4928 | variable |
\theta_{\rm Brewster}
\(\theta_{\rm Brewster}\) |
['real'] | dimensionless | Brewster's angle | 16 |