💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Like

Report

WZ
Numerade Educator

Like

Report

Problem 52 Hard Difficulty

Suppose the three coordinate planes are all mirrored and a light ray given by the vector $ a = \langle a_1, a_2, a_3 \rangle $ first strikes the $ xz $-plane, as shown in the figure. Use the fact that the angle of incidence equals the angle of reflection to show that the direction of the reflected ray is given by $ b = \langle a_1, -a_2, a_3 \rangle $. Deduce that, after being reflected by all three mutually perpendicular mirrors, the resulting ray is parallel to the initial ray. (American space scientists used this principle, together with laser beams and an array of corner mirrors on the moon, to calculate very precisely the distance from the earth to the moon.)

Answer

$$
\mathbf{d}=\left\langle- a_{1},-a_{2},-a_{3}>=(-1)<a_{1}, a_{2}, a_{3}>=(-1) \mathbf{a}\right.
$$

Discussion

You must be signed in to discuss.

Video Transcript

The problem is suppose the three coordinates planes are on me. Rid and alight, agreed. Human lies. The walk to a seat could be wanted to a three firsts tracks The axe a pipeline has shown in the figure use the fact that it's an angle of incidence in coast. To the angle of reflection. She showed that the direction of the respective three is killing by B. It's a photo. A one negative two three deduce that after being reflected back off three marginally Antiqua mirrors There is out. Henry is parent out to the initial reed for this problem, please. We only need the direction of out of fractures in the city. We don't need two magnitude. Have are the doctors. So for simplicity here we can assume out of lecture for our actors. Their magnitude are the scene then, Okada, this graph This's a taxi plane on DH. Back to a on director Being these is to tango, she wrangles Yuko. So we have this one too. This is a class B. Is this true angles? Because all this two angles article So we have this collector. So a plus b Is this like two A plus B It's perpendicular. She's a normal actor off extreme plane on DH Negative a plus speed. So is this, like, two? Its power. Now she's a normal actor And here's a reason Nice faces, true angles ICO So we half this two angles, Nico, and as the properties of parallelogram with half this too Segments Are you cold? It's romantic on DH Thiss two angles are equal. This is anti cure We have just two properties Then Now move back Chur us angsty plane. And here too. Zero one Cyril. So first we assume. Is he going to be one? Me too green Well, half from this one. Behalf each you us a too has lan is equal to cereal. So each is a contra negative and two from this property we have They want class B one negative one class B one four two zero Negative three plus p three s a caught you, Sarah. So you want to say to anyone The three. You see what you in three we have This is I'm blind. Negative too A three. So be it. They want negative into three then similarly we have Dr C. It's the culture you want negative. A too negative. A three on DH, much d. It's equal to Conectiv. Want connective too negative. Three. So what d is para now, too? The laughter.