Into Air — phryzby

Q. Light leaves a medium of index μ₁ for air at 30°. Does every medium have its own angle?

What the draft establishes

Fills in once a draft is checked.

The web of concepts

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The equations it used

None yet.

Check an answer

Q. Light leaves a medium of index $μ_{1}$ for air $μ_{2} = 1$ at 30° $i = 30 °$ . Does every medium have its own angle?

The solution

Solved with Reflection, Refraction

Given

$i = 30 °$
$μ_{2} = 1$ from “air”
$μ_{1}$ yours to vary

Find $c$ , $r_{r}$ , whether there is no refracted ray.

Working

snells law when grazing exit $μ_{1} \cdot \sin c = μ_{2} \cdot \sin 90 °$
$1.33 \cdot \sin c = 1 \cdot \sin 90 °$
$c = 48.75°$
snells law $μ_{1} \cdot \sin i = μ_{2} \cdot \sin r_{r}$
$1.33 \cdot \sin 30 ° = 1 \cdot \sin r_{r}$
$r_{r} = 41.68°$
no refracted ray? $i > c$ no

Conclusion

Every medium has one of its own, and the denser the medium the sooner it stops letting light out.

The Ruby

1require_relative "../physics"23question :into_air do4  describes "Light leaves a medium of index %{index} for air at %{angle}. Does every medium have %{critical_angle}?"5  given :index6  given angle: "30 deg"7  asks critical_angle: "its own angle"8end

1require_relative "../questions/into_air"2require_relative "../science/ray_optics_and_optical_instruments/reflection"3require_relative "../science/ray_optics_and_optical_instruments/refraction"4require_relative "../science/ray_optics_and_optical_instruments/refractive_media"56solve :into_air, using: [ Reflection, Refraction ] do7  take index: :mu_1, angle: :i8  deduce_from "air", mu_2: REFRACTIVE_MEDIA.fetch("air")9  take critical_angle: :c10  find_value :critical_angle11  find_value :r_r12  find_whether :no_refracted_ray?1314  conclusion "Every medium has one of its own, and the denser the medium the sooner it stops letting light out."15end

1require_relative "../solutions/into_air"2require_relative "../science/ray_optics_and_optical_instruments/refractive_media"3require_relative "../pictures/light"45play_with :into_air do6  title "Into Air"78  input :from, REFRACTIVE_MEDIA, default: "water"910  input(:mu_1) { from }1112  output :c13  output :r_r14  output :no_refracted_ray?, alarm: true1516  draw Light::Picture, rising: true do17    media :from, "air"18    ray "incident",  arriving_at: :i, angle: true19    ray "reflected", leaving_at:  :r_l20    ray "refracted", crossing_at: :r_r, angle: true, unless: :no_refracted_ray?21    mark "critical", arriving_at: :c22    note "all of it turns back", 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
angle of reflection	$r_{l}$	—	0 … 1.571	Reflection
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_{l} \equiv θ_{i} (after)

angle of reflection

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

i = r_{l}

law of reflection

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?