From: Andrew Lorimer Date: Sat, 4 Aug 2018 12:30:47 +0000 (+1000) Subject: double-slit experiment and em waves X-Git-Tag: yr11~76 X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/b7926ced05f2edce311cddadb8155f132e5a0fc7?hp=30b2c80b12f81ebba914334f500e199b3c3aaa89 double-slit experiment and em waves --- diff --git a/physics/graphics/double-slit-interference.png b/physics/graphics/double-slit-interference.png new file mode 100644 index 0000000..b3fea7a Binary files /dev/null and b/physics/graphics/double-slit-interference.png differ diff --git a/physics/graphics/double-slit.png b/physics/graphics/double-slit.png new file mode 100644 index 0000000..2e90ca0 Binary files /dev/null and b/physics/graphics/double-slit.png differ diff --git a/physics/graphics/em-waves.png b/physics/graphics/em-waves.png new file mode 100644 index 0000000..2db7ba6 Binary files /dev/null and b/physics/graphics/em-waves.png differ diff --git a/physics/graphics/field-lines.png b/physics/graphics/field-lines.png new file mode 100755 index 0000000..57abf1e Binary files /dev/null and b/physics/graphics/field-lines.png differ diff --git a/physics/graphics/huygen.png b/physics/graphics/huygen.png new file mode 100644 index 0000000..9168dc0 Binary files /dev/null and b/physics/graphics/huygen.png differ diff --git a/physics/graphics/longitudinal-waves.png b/physics/graphics/longitudinal-waves.png new file mode 100644 index 0000000..9133b1b Binary files /dev/null and b/physics/graphics/longitudinal-waves.png differ diff --git a/physics/graphics/rays.png b/physics/graphics/rays.png new file mode 100644 index 0000000..91be132 Binary files /dev/null and b/physics/graphics/rays.png differ diff --git a/physics/graphics/refraction.png b/physics/graphics/refraction.png new file mode 100644 index 0000000..5842e19 Binary files /dev/null and b/physics/graphics/refraction.png differ diff --git a/physics/graphics/transverse-waves.png b/physics/graphics/transverse-waves.png new file mode 100644 index 0000000..540220d Binary files /dev/null and b/physics/graphics/transverse-waves.png differ diff --git a/physics/waves.md b/physics/waves.md index f082d0f..d0d795c 100644 --- a/physics/waves.md +++ b/physics/waves.md @@ -1,7 +1,7 @@ # Waves ## Mechanical waves -- need a medium to travel through +- need a medium to travel through (fields for electromagnetic waves) - cannot transfer energy through vacuum - individual particles have little movement regardless of the distance of wave - **transfer of energy without net transfer of matter** @@ -15,13 +15,13 @@ **Direction of motion is parallel to wave** -![](/mnt/andrew/graphics/longitudinal-waves.png) +![](graphics/longitudinal-waves.png) ### Transverse waves **Direction of motion is perpendicular to wave** - rarefactions (expansions) - compressions -![](/mnt/andrew/graphics/transverse-waves.png) +![](graphics/transverse-waves.png) ### Measuring mechanical waves @@ -38,7 +38,7 @@ $v=f \lambda \quad$(speed: displacement per second) - applies to all types of wave - only affects apparent $f$; actual $f$ is constant -When $P_1$ approaches $P_2$, each wave $w_n$ has slightly less distance to travel than $w_{n-1}. Hence, $w_n$ reaches the observer sooner than $w_{n-1}, increasing "apparent" wavelength. +When $P_1$ approaches $P_2$, each wave $w_n$ has slightly less distance to travel than $w_{n-1}$. Hence, $w_n$ reaches the observer sooner than $w_{n-1}$, increasing "apparent" wavelength. @@ -64,7 +64,7 @@ Two- or three-dimensional *wave fronts* can be reflected, e.g. waves at a beach. Direction of motion of wave fronts can be shown by arrows, called *rays*, which are perpendicular to the wave front: -![](/mnt/andrew/graphics/rays.png) +![](graphics/rays.png) Angle of incidence $\theta_i =$ angle of reflection $\theta_r$ - Normal: $\perp$ to wall @@ -90,8 +90,6 @@ $f = {nv \div 4l}\quad$ (frequency for $n_{th}$ harmonic at length $l$ and speed ## Light - - Newton - light as a particle - light speeds up as it travels through a solid medium @@ -100,15 +98,15 @@ Hooke - light as a wave ### Huygen's principle **Each point on a wavefront can be considered a source of secondary wavelets** -![](/mnt/andrew/graphics/huygen.png) +![](graphics/huygen.png) ### Refraction **Change in direction caused by change in speed** e.g. prism $\Delta v$ depends on $\lambda$, so wavelengths become "split" -![](/mnt/andrew/graphics/refraction.png) +![](graphics/refraction.png) Refractive index of a medium depends $\Delta v$ from $c$ -$n={c \over v}\quad$ (refractive index of poop medium) +$n={c \over v}\quad$ (refractive index of medium) $n_1v_1=n_2v_2$ (equivalence between media) ### Snell's law @@ -127,8 +125,44 @@ $\therefore \theta_c = {n_2 \over n_1}$ ### Double Slit +![](graphics/double-slit.png) +**(a) Double slit as theorised by particle model** - "streams" of photons are concentrated in bright spots +**(b) Double slit as theorised by wave model** - waves disperse onto screen (overlapping) + +Young's double slit experiment supports wave model: - 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 +- fringes - points of constructive interference (bright) +- constructive interference when waves are **coherent** (in phase) +- fringe in centre of slits - solve path difference using pythag + +![](graphics/double-slit-interference.png) + +Path difference $pd = |S_1P-S_2P|$ for point $p$ on screen + +Constructive interference when $pd = n\lambda$ where $n \in [0, 1, 2, ...]$ +Destructive interference when $pd = (n-{1 \over 2})\lambda$ where $n \in [1, 2, 3, ...]$ + +Fringe separation: +$$\Delta x = {{\lambda l }\over d}$$ + +where +$\Delta x$ is distance between fringes +$l$ is distance from slits to screen +$d$ is separation between sluts ($=S_1-S_2$) + +## Electromagnetic waves + +![](graphics/em-waves.png) + +- electric waves and magnetic waves are perpendicular to each other due to Faraday's law + +Wave equation: + +$$c = f \lambda$$ + +where +$c$ is velocity (speed of light in this case) +$f$ is frequency (Hz) +$\lambda$ is wavelength (m)