Refraction: Water to Air

Q. Light in water meets air at i. Which way does it bend coming out?

What the draft establishes

Fills in once a draft is checked.

The web of concepts

given read from the words equation asked

The equations it used

None yet.

Check an answer

Q. Light in water $μ_{1} = 1.33$ meets air $μ_{2} = 1$ at $i$ . Which way does it bend coming out?

The playground

Inputs

angle of incidence

i

45.00°

Outputs

angle of refraction

r_{r}

70.13°

no refracted ray?no

The solution

Solved with Refraction

Given

$μ_{1} = 1.33$ from “water”
$μ_{2} = 1$ from “air”
$i$ yours to vary

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

Working

snells law $μ_{1} \cdot \sin i = μ_{2} \cdot \sin r_{r}$
$1.33 \cdot \sin 45 ° = 1 \cdot \sin r_{r}$
$r_{r} = 70.13°$
snells law when grazing exit $μ_{1} \cdot \sin c = μ_{2} \cdot \sin 90 °$
$1.33 \cdot \sin c = 1 \cdot \sin 90 °$
$c = 48.75°$
no refracted ray? $i > c$ no

Conclusion

It bends away from the normal instead, and far enough round there is no way across at all.

The Ruby

1require_relative "../physics"23question :water_to_air do4  describes "Light in water meets air at %{angle}. %{refracted}?"5  given :angle6  asks refracted: "Which way does it bend coming out"7end

1require_relative "../questions/water_to_air"2require_relative "../science/ray_optics_and_optical_instruments/refraction"3require_relative "../science/ray_optics_and_optical_instruments/refractive_media"45solve :water_to_air, using: Refraction do6  take angle: :i7  deduce_from "water", mu_1: REFRACTIVE_MEDIA.fetch("water")8  deduce_from "air", mu_2: REFRACTIVE_MEDIA.fetch("air")9  take refracted: :r_r10  find_value :refracted11  find_whether :no_refracted_ray?1213  conclusion "It bends away from the normal instead, and far enough round there is no way across at all."14end

1require_relative "../solutions/water_to_air"2require_relative "../science/ray_optics_and_optical_instruments/refractive_media"3require_relative "../pictures/light"45play_with :water_to_air do6  title "Refraction: Water to Air"78  input :i, default: 45.deg910  output :r_r11  output :no_refracted_ray?, alarm: true1213  draw Light::Picture, rising: true do14    media "water", "air"15    ray "incident",  arriving_at: :i,  angle: true, extended: true16    ray "refracted", crossing_at: :r_r, angle: true, unless: :no_refracted_ray?17    note "no refracted ray", when: :no_refracted_ray?18  end19end

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?