From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Fri, 17 Aug 2018 02:55:14 +0000 (+1000)
Subject: tangents & normals, light-matter interactions
X-Git-Tag: yr11~65^2~1
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/08a48a51e451aa322afd0efec300e5010a6bffec

tangents & normals, light-matter interactions
---

diff --git a/methods/calculus.md b/methods/calculus.md
index fb19fdb..589bf2f 100644
--- a/methods/calculus.md
+++ b/methods/calculus.md
@@ -48,3 +48,23 @@ Instantaneous velocity - calculated the same way as averge $\Delta$
 $$f^\prime(x)=\lim_{h \rightarrow 0}{{f(x+h)-f(x)} \over h}$$
 
 **Tangent line** of function $f$ at point $M(a, f(a))$ is the line through $M$ with gradient $f^\prime(a)$.
+
+## Tangents and gradients
+
+
+### Tangent of a point
+
+For a point $P(q,r)$ on function $f$, the gradient of the tangent is the derivative $dy \over dx$ of $f(q)$. Therefore the tangent line is defined by $y=mx+c$ where $m={dy \over dx}$. Substitute $x=q, \hspace{0.5em} y=q$ to solve for $c$.
+
+### Normal
+
+Normal $\perp$ tangent.
+
+$$m_{\operatorname{tan}} \cdot m_{\operatorname{norm}} = -1$$
+
+Normal line for point $P(q,r)$ on function $f$ is $y=mx+c$ where $m={-1 \over m_{\tan}}$. To find $c$, substitute $(x, y)=(q,r)$ and solve.
+
+### Solving on CAS
+
+**In main**: type function. Interactive -> Calculation -> Line -> (Normal | Tan line)  
+**In graph**: define function. Analysis -> Sketch -> (Normal | Tan line). Type $x$ value to solve for a point. Return to show equation for line.
diff --git a/physics/light-matter.md b/physics/light-matter.md
new file mode 100644
index 0000000..04a90a4
--- /dev/null
+++ b/physics/light-matter.md
@@ -0,0 +1,28 @@
+# Light and matter
+
+## Photoelectric effect
+
+### Planck's equation
+
+$$E=hf$$
+
+where  
+$E$ is energy of a quantum of light (J)  
+$f$ is frequency of EM radiation
+$h$ is Planck's constant ($6.63 \times 10^{-34}\operatorname{J s}$)
+
+
+### Electron diffraction patterns
+
+$$W=qV$$
+
+(work for accelerating electon of charge $q$ with voltage $V$)
+
+$$\lambda = {h \over mv}$$
+
+(de Broglie's equation)
+
+Solving wavelength of electrons from gun:
+1.
+
+774 abc melbourne
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