wave interference, minor adjustments to locus notes

diff --git a/physics/waves.md b/physics/waves.md
index 8f94d828e04e1372b50051efee32206ea855d83c..f082d0f2d326fcfd98548cb701852bbc9341f0f1 100644 (file)
--- a/physics/waves.md
+++ b/physics/waves.md
@@ -108,7 +108,7 @@ $\Delta v$ depends on $\lambda$, so wavelengths become "split"
 ![](/mnt/andrew/graphics/refraction.png)
 
 Refractive index of a medium depends $\Delta v$ from $c$
-$n={c \over v}\quad$ (refractive index of a medium)
+$n={c \over v}\quad$ (refractive index of  poop medium)
 $n_1v_1=n_2v_2$ (equivalence between media)
 
 ### Snell's law
@@ -124,3 +124,11 @@ $n_1 sin \theta_c = n_2 \sin 90^\circ$
 $\therefore \theta_c = {n_2 \over n_1}$
 
 ### Dispersion
+
+### Double Slit
+
+- parallel slits of thickness comparable to $\lambda$
+- multiple wave fronts combine to form constructive / destructive interference
+- fringes - points of constructive interference
+- bright spot in centre of slits
+- solve path difference using pythag

diff --git a/spec/graphing.md b/spec/graphing.md
index 6cd013e79389e1a7f92b4a8566f0d4c3c2032e60..39b748d0ffe73a8e18c3d41eb18347a0be3737bc 100644 (file)
--- a/spec/graphing.md
+++ b/spec/graphing.md
@@ -94,6 +94,8 @@ $${(x-h)^2 \over a^2} - {(y-k)^2 \over b^2} = 1$$
 Asymptotes at $y=\pm {b \over a}(x-h)+k$
 To make hyperbola up/down rather than left/right, swap $x$ and $y$
 
+$y^2-x^2=1$ produces hyperbola shifted 90 $^\circ$ (top and bottom of asymptotes)
+
 ## Parametric equations
 
 Parametric curve:
@@ -101,3 +103,46 @@ Parametric curve:
 $$x=f(t), \quad y=g(t)$$
 
 $t$ is the parameter
+
+## Polar coordinates
+
+$$x = r\cos\theta, \quad y = r\sin\theta$$
+
+### Spirals
+$$r={\theta \over n\pi}$$
+- solve intercepts for multiples of $\pi \over 2$
+- or draw table of values for $r$ and $\theta$ for each $n\pi \over 2$
+
+### Circles
+$$r=a$$
+
+### Lines
+
+Horizontal: $r={n \over \sin \theta}$
+Vertical: $r={n \over \cos \theta}$
+
+### Solving polar graphs
+
+solve in terms of $r$
+
+e.g. $x=4$
+$r\cos\theta = 4$
+$r={4 \over \cos\theta}$
+
+e.g. $y=x^2$
+$r\sin\theta = r^2 \cos^2 \theta$
+$\sin \theta = r \cos^2 \theta$
+$r = {\sin \theta \over \cos^2\theta} = \tan\theta \sec\theta$
+
+e.g. $r=6\cos \theta\quad$ *(multiple by $r$)*
+$r^2=6r\cos\theta$
+$x^2+y^2=6x$
+complete the square
+
+## Other graphs
+
+### Cardioids
+
+$$
+
+### Roses