QR question - reflected light

[lala05]

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The side of a square is equal to 10 units. The four inner sides of the square are mirrored surfaces that reflect light internally. A light beam originates at (0,3) and strikes the bottom at (2,0). At what x-coordinate will the beam next strike the bottom of the box? (photo attached)

 

[RCT PC CRN]

(14/3, 0)


Edit: Sorry to put the answer only. I was in rush.

 

[herkulease]

where do you even begin with this problem?

the only thing I can think of is using the slope from the 1st one. its -1.5 which would mean when the beam hits the top it the slope shoudl be 1.5, when it comes back down it should be -1.5.

how to determine the points. I have no idea or forgot the formula.

 

[LuckMC11]

yea how did u do this RCT?

would we see something like this on teh test?

 

[RCT PC CRN]

I seriously doubt if I will see something like this on real DAT. If I do see I'm putting it for last. From the first encounter, it took me about 2-3 min to get the answer.

I think what I got (14/3, 0) is correct answer. If lala can confirm that.

Basically it's equal angle triangle problem. Where it says that if you have 2 triangle with same 3 angle measurement then their sides will be in proportion. With reflexion of rays you get equal angles. So that's what basically you are playing with.

It's hard to explain here in words since it's geometry. Try to follow light ray and create couple of triangles, do some simple math, you should be able to get the answer. Remember, you will have triangles with same angle measurements so the sides will be in proportion.

 

[RCT PC CRN]

Where did you see this lala?

 

[lala05]

Where did you see this lala?

I apologize, I forgot to include the answer. You both are correct - the answer is x = 14/3.


It was on the 2009 ADA sample test. I'm starting to freak out since I've never seen anything like this before in my study books!

 

[Vinden]

I seriously doubt if I will see something like this on real DAT. If I do see I'm putting it for last. From the first encounter, it took me about 2-3 min to get the answer.

I think what I got (14/3, 0) is correct answer. If lala can confirm that.

Basically it's equal angle triangle problem. Where it says that if you have 2 triangle with same 3 angle measurement then their sides will be in proportion. With reflexion of rays you get equal angles. So that's what basically you are playing with.

It's hard to explain here in words since it's geometry. Try to follow light ray and create couple of triangles, do some simple math, you should be able to get the answer. Remember, you will have triangles with same angle measurements so the sides will be in proportion.

I got the same answer!🙂

 

[lala05]

can someone please explain briefly how you got the answer? I'm going crazy trying to figure it out😡

 

[2ndFn]

I remember seeing a reflected light question in Achiever, not sure if it is QR4 or 5. The solution explains pretty well there using both graphical and mathematical approaches. Check it out, folks.

 

[Streetwolf]

Any time it reflects, the slope just changes from positive to negative. That means there's always the same ratio of up/down to right/left. Therefore, if we know the distance up/down that we need to travel, we know the distance right/left it will take.

We start at (0,3), sink down to the bottom (y-coord 0), rise up to the top (y-coord 10), and sink down to the bottom (y-coord 0) for a total distance of 23 units up/down.

With 3 units up/down for every 2 right/left, we go (23/3) * 2 = 46/3 units right/left. (Remember this is starting from the beginning of the graph at (0,3) and not anywhere beyond that.)

The square maxes out at 10 units long = 30/3. So on the way back left, it travels 46/3 - 30/3 = 16/3 FROM THE RIGHT. This places us at (14/3, 0).

 

[lala05]

Any time it reflects, the slope just changes from positive to negative. That means there's always the same ratio of up/down to right/left. Therefore, if we know the distance up/down that we need to travel, we know the distance right/left it will take.

We start at (0,3), sink down to the bottom (y-coord 0), rise up to the top (y-coord 10), and sink down to the bottom (y-coord 0) for a total distance of 23 units up/down.

With 3 units up/down for every 2 right/left, we go (23/3) * 2 = 46/3 units right/left. (Remember this is starting from the beginning of the graph at (0,3) and not anywhere beyond that.)

The square maxes out at 10 units long = 30/3. So on the way back left, it travels 46/3 - 30/3 = 16/3 FROM THE RIGHT. This places us at (14/3, 0).

wow my brain hurts, but I finally get it. Thank you Streetwolf!