Refractive Index

Q. Light passes from a medium of index μ₁ into one of μ₂ at 30°. Where does the bending come from?

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Q. Light passes from a medium of index $μ_{1}$ into one of $μ_{2}$ at 30° $i = 30 °$ . Where does the bending come from?

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Inputs

refractive index of first medium

μ_{1}

1.33water

refractive index of second medium

μ_{2}

1air

Outputs

critical angle

c

48.75°

angle of refraction

r_{r}

41.68°

no refracted ray?no

The solution

Solved with Reflection, Refraction

Given

$i = 30 °$
$μ_{1}$ , $μ_{2}$ 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

From one number each. Every medium has its own, the law asks for both, and everything the last five chapters held fixed was a pair of them.

The Ruby

1require_relative "../physics"23question :refractive_index do4  describes "Light passes from a medium of index %{first_index} into one of %{second_index} at %{angle}. Where does %{refracted} come from?"5  given :first_index6  given :second_index7  given angle: "30 deg"8  asks refracted: "the bending"9end

1require_relative "../questions/refractive_index"2require_relative "../science/ray_optics_and_optical_instruments/reflection"3require_relative "../science/ray_optics_and_optical_instruments/refraction"45solve :refractive_index, using: [ Reflection, Refraction ] do6  take first_index: :mu_1, second_index: :mu_2, angle: :i7  find_value :c8  take refracted: :r_r9  find_value :refracted10  find_whether :no_refracted_ray?1112  conclusion "From one number each. Every medium has its own, the law asks for both, and everything the last five chapters held fixed was a pair of them."13end

1require_relative "../solutions/refractive_index"2require_relative "../science/ray_optics_and_optical_instruments/refractive_media"3require_relative "../pictures/light"45INDEX = 1.0..4.067play_with :refractive_index do8  title "Refractive Index"910  input :mu_1, INDEX, default: 1.33, marks: REFRACTIVE_MEDIA11  input :mu_2, INDEX, default: 1.0, marks: REFRACTIVE_MEDIA1213  output :c14  output :r_r15  output :no_refracted_ray?, alarm: true1617  draw Light::Picture, rising: true do18    media :mu_1, :mu_219    ray "incident",  arriving_at: :i, angle: true20    ray "reflected", leaving_at:  :r_l21    ray "refracted", crossing_at: :r_r, angle: true, unless: :no_refracted_ray?22    mark "critical", arriving_at: :c23    note "all of it turns back", when: :no_refracted_ray?24  end25end

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?