## Welcome to BrainDen.com - Brain Teasers Forum

 Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account. As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends. Of course, you can also enjoy our collection of amazing optical illusions and cool math games. If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top. If you have a website, we would appreciate a little link to BrainDen. Thanks and enjoy the Den :-)
Guest Message by DevFuse

# The "aha!" problems 8: Reflect on this

Best Answer Rob_G, 22 May 2014 - 04:54 PM

Spoiler for Hmm...

Go to the full post

13 replies to this topic

### #11 Rob_G

Rob_G

Junior Member

• Members
• 29 posts

Posted 23 May 2014 - 03:30 PM

Spoiler for I came up with this...

Edited by Rob_G, 23 May 2014 - 03:31 PM.

• -1

### #12 m00li

m00li

Junior Member

• Members
• 71 posts

Posted 23 May 2014 - 10:41 PM

Yes, bonanova. I think the answer depends on a (e.g. if a is obtuse the ray doesnt exit on left and never hits the top mirror). It coinicides with the icident ray if a is a factor of pi/2 radian

Everything in your post is correct. But remember what the question is.

Whatever value a has, how close does the ray come to the point O?

The phrase "before it exits to the left" is appropriate to a being acute, as in the figure.

If you want to include a being obtuse, so that the ray would not exit to the left,

that just gives you "forever" as the time frame to consider the ray's point of closest approach.

Although of course you wouldn't need "forever" to determine it.

In other words, the wording is not meant to be tricky: assume a to be acute if you like.

Hi Bonanova,

Sorry, I do not understand. Is my answer wrong? or incomplete?

• 0

### #13 bonanova

bonanova

bonanova

• Moderator
• 5918 posts
• Gender:Male
• Location:New York

Posted 25 May 2014 - 12:13 AM

I probably muddied the waters by at first specifying a to be 22.5o. My bad.

It got people to worry about the exiting trajectory of the ray, a matter that is irrelevant to the question asked.

The Aha! question asks (only) for the distance from the ray to the point
O at its point of closest approach. The Aha! moment comes with the realization that this distance has no dependence whatsoever on the value of a.

Spoiler for Why this is so

• 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

### #14 m00li

m00li

Junior Member

• Members
• 71 posts

Posted 25 May 2014 - 01:58 AM

understood the exact question now

• 0

#### 0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users