Reflection — phryzby

solved Reflection

Q. Where does a ray go when it hits a mirror at $i$ ?

Inputs

angle of incidence

i

30.00°

Outputs

angle of reflection

r_{l}

30.00°

How it's solved

Solved with Reflection

Given

$i$ yours to vary

Find $r_{l}$ .

Working

law of reflection $i = r_{l}$
$30 ° = r_{l}$
$r_{l} = 30.00°$

Conclusion

Back out at the angle it came in at, on the other side of the normal, and all of it goes back.

The web of concepts

given read from the words equation asked

The Ruby that solves it

The question and its solution are small Ruby files. The engine runs them.

question.rb

1require_relative "../physics"23question :reflection do4  describes "%{reflected} when it hits a mirror at %{angle}?"5  given :angle6  asks reflected: "Where does a ray go"7end

solution.rb

1require_relative "../questions/reflection"2require_relative "../science/ray_optics_and_optical_instruments/reflection"34solve :reflection, using: Reflection do5  take angle: :i6  take reflected: :r_l7  find_value :reflected89  conclusion "Back out at the angle it came in at, on the other side of the normal, and all of it goes back."10end

playground.rb

1require_relative "../solutions/reflection"2require_relative "../pictures/light"34play_with :reflection do5  title "Reflection"67  input :i, default: 30.deg89  output :r_l1011  draw Light::Picture do12    mirror13    ray "incident",  arriving_at: :i, angle: true14    ray "reflected", leaving_at:  :r_l, angle: true15  end16end

The laws it drew on

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

i \equiv θ_{i} (before)

angle of incidence

r_{l} \equiv θ_{i} (after)

angle of reflection

i = r_{l}

law of reflection