Internal Reflection

Q. Light in water meets air at i. What happens to the light that is not refracted?

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 $i$ . What happens to the light that is not refracted?

The playground

Inputs

angle of incidence

i

60.00°

Outputs

angle of reflection

r_{l}

60.00°

angle of refraction

r_{r}

—

no refracted ray?yes

The solution

Solved with Reflection, Refraction

Given

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

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

Working

law of reflection $i = r_{l}$
$60 ° = r_{l}$
$r_{l} = 60.00°$
snells law when grazing exit $μ_{1} \cdot \sin c = μ_{2} \cdot \sin 90 °$
$1.33 \cdot \sin c = 1 \cdot \sin 90 °$
$c = 48.75°$
$r_{r} = —$
no refracted ray? $i > c$ yes

Conclusion

It turns back into the water, and past this angle that is all of the light: the surface is a mirror. Slide down and the other ray returns, because some of it turns back at every angle.

The Ruby

1require_relative "../physics"23question :internal_reflection do4  describes "Light in water meets air at %{angle}. %{reflected}?"5  given :angle6  asks reflected: "What happens to the light that is not refracted"7end

1require_relative "../questions/internal_reflection"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 :internal_reflection, using: [ Reflection, Refraction ] do7  take angle: :i8  deduce_from "water", mu_1: REFRACTIVE_MEDIA.fetch("water")9  deduce_from "air", mu_2: REFRACTIVE_MEDIA.fetch("air")10  take reflected: :r_l11  find_value :reflected12  find_value :r_r13  find_whether :no_refracted_ray?1415  conclusion "It turns back into the water, and past this angle that is all of the light: the surface is a mirror. Slide down and the other ray returns, because some of it turns back at every angle."16end

1require_relative "../solutions/internal_reflection"2require_relative "../science/ray_optics_and_optical_instruments/refractive_media"3require_relative "../pictures/light"45play_with :internal_reflection do6  title "Internal Reflection"78  input :i, default: 60.deg910  output :r_l11  output :r_r12  output :no_refracted_ray?, alarm: true1314  draw Light::Picture, rising: true do15    media "water", "air"16    ray "incident",  arriving_at: :i,  angle: true17    ray "reflected", leaving_at:  :r_l, angle: true18    ray "refracted", crossing_at: :r_r, angle: true, unless: :no_refracted_ray?19    note "all of it turns back", when: :no_refracted_ray?20  end21end

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?