Refraction: Air to Water

Q. Where does a ray go when it passes from air into water at i?

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. Where does a ray go when it passes from air $μ_{1} = 1$ into water $μ_{2} = 1.33$ at $i$ ?

The playground

Inputs

angle of incidence

i

60.00°

Outputs

angle of refraction

r_{r}

40.63°

The solution

Solved with Refraction

Given

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

Find $r_{r}$ .

Working

snells law $μ_{1} \cdot \sin i = μ_{2} \cdot \sin r_{r}$
$1 \cdot \sin 60 ° = 1.33 \cdot \sin r_{r}$
$r_{r} = 40.63°$

Conclusion

It goes through, and bends toward the normal doing so. The two angles are neither equal nor proportional: what each medium does to the sine of its own angle, the other undoes.

The Ruby

1require_relative "../physics"23question :refraction do4  describes "%{refracted} when it passes from air into water at %{angle}?"5  given :angle6  asks refracted: "Where does a ray go"7end

1require_relative "../questions/refraction"2require_relative "../science/ray_optics_and_optical_instruments/refraction"3require_relative "../science/ray_optics_and_optical_instruments/refractive_media"45solve :refraction, using: Refraction do6  take angle: :i7  deduce_from "air", mu_1: REFRACTIVE_MEDIA.fetch("air")8  deduce_from "water", mu_2: REFRACTIVE_MEDIA.fetch("water")9  take refracted: :r_r10  find_value :refracted1112  conclusion "It goes through, and bends toward the normal doing so. The two angles are neither equal nor proportional: what each medium does to the sine of its own angle, the other undoes."13end

1require_relative "../solutions/refraction"2require_relative "../science/ray_optics_and_optical_instruments/refractive_media"3require_relative "../pictures/light"45play_with :refraction do6  title "Refraction: Air to Water"78  input :i, default: 60.deg910  output :r_r1112  draw Light::Picture do13    media "air", "water"14    ray "incident",  arriving_at: :i,  angle: true, extended: true15    ray "refracted", crossing_at: :r_r, angle: true16  end17end

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?