Any Two Media — phryzby

How it's solved

Solved with Refraction

Given

$i = 20 °$
$μ_{1}$ , $μ_{2}$ yours to vary

Find whether there is bends toward the normal, whether there is bends away from the normal, whether there is no refracted ray.

Working

snells law $μ_{1} \cdot \sin i = μ_{2} \cdot \sin r_{r}$
$1 \cdot \sin 20 ° = 1.5 \cdot \sin r_{r}$
$r_{r} = 13.18°$
bends toward the normal? $r_{r} < i$ yes
bends away from the normal? $r_{r} > i$ no
no refracted ray? $i > c$ no

Conclusion

They bend it, and which way follows from which of them is the denser.

The web of concepts

given read from the words equation asked

The Ruby that solves it

The question and its solution are small Ruby files. The engine runs them.

question.rb

1require_relative "../physics"23question :any_two_media do4  describes "A ray meets the boundary between two media, of indices %{first_index} and %{second_index}, at %{angle}. What " \5          "do they do to it?"6  given :first_index7  given :second_index8  given angle: "20 deg"9end

solution.rb

1require_relative "../questions/any_two_media"2require_relative "../science/ray_optics_and_optical_instruments/refraction"34solve :any_two_media, using: Refraction do5  take first_index: :mu_1, second_index: :mu_2, angle: :i6  find_whether :bends_toward_the_normal?7  find_whether :bends_away_from_the_normal?8  find_whether :no_refracted_ray?910  conclusion "They bend it, and which way follows from which of them is the denser."11end

playground.rb

1require_relative "../solutions/any_two_media"2require_relative "../science/ray_optics_and_optical_instruments/refractive_media"3require_relative "../pictures/light"45play_with :any_two_media do6  title "Any Two Media"78  input :from, REFRACTIVE_MEDIA9  input :into, REFRACTIVE_MEDIA, default: "glass"1011  input(:mu_1) { from }12  input(:mu_2) { into }1314  output :bends_toward_the_normal?15  output :bends_away_from_the_normal?16  output :no_refracted_ray?, alarm: true1718  draw Light::Picture do19    media :from, :into20    ray "incident",  arriving_at: :i, extended: true21    ray "refracted", crossing_at: :r_r, unless: :no_refracted_ray?22    note "no refracted ray", when: :no_refracted_ray?23  end24end

quantity	written	units	within	from
angle to the normal	$θ$	—	0 … 1.571	Incidence
angle of incidence	$i$	—	0 … 1.571	Incidence
refractive index	$μ$	—	—	Refraction
angle of refraction	$r_{r}$	—	0 … 1.571	Refraction
refractive index of first medium	$μ_{1}$	—	—	Refraction
refractive index of second medium	$μ_{2}$	—	—	Refraction
critical angle	$c$	—	0 … 1.571	Refraction