Any Two Media — phryzby

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Q. A ray meets the boundary between two media, of indices μ₁ and μ₂, at 20°. What do they do to it?

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Q. A ray meets the boundary between two media, of indices $μ_{1}$ and $μ_{2}$ , at 20° $i = 20 °$ . What do they do to it?

The solution

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 Ruby

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

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

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

The laws

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

i \equiv θ_{i} (before)

angle of incidence

r_{r} \equiv θ_{i} (after)

angle of refraction

μ_{1} \equiv μ_{b}

refractive index of first medium

μ_{2} \equiv μ_{a}

refractive index of second medium

μ_{1} \cdot \sin i = μ_{2} \cdot \sin r_{r}

snells law

μ_{1} \cdot \sin c = μ_{2} \cdot \sin 90 °

snells law when grazing exit

r_{r} = 90 °

grazing exit?

i > c

no refracted ray?

r_{r} < i

bends toward the normal?

r_{r} > i

bends away from the normal?