Take One 2m Reflective Hollow Sphere

[German_EE]

I get asked some of the craziest questions by a neighbor's kid who is at a very impressionable age, he wants to become an engineer and he's interested in everything. So, after experimenting with a junk Christmas ornament he has the following question:

You're in the center of a very large glass Christmas ball and the inner surface of the thing is a mirror. You turn on your torch, what do you see?

My initial answer was that the sphere would be filled with light but then I thought about a) the shadow I would cast behind me and b) How I would look reflected by a hemispherical mirror, then it got really complicated.

All ideas and opinions welcome.

[BravoV]

Do a raytracing rendering for the result like Blender maybe ? 

[Kire Pûdsje]

Vsauce: inside a spherical mirror.

[cdev]

There is a complete inversion of whatever is at the other nodal point.

Like when you are in a perfectly round room you can hear somebody whisper on the other side at exactly where you are. Visually, it would be inverted in both directions.

Dave could use the images he uploaded of his head, map them to a head shape and then render that inside a mirrored sphere.

Bet Sagan would get a kick out of that!

[Mr. Scram]

Do a raytracing rendering for the result like Blender maybe ? 

It's a good idea, but won't work. You set a limited amount of bounces, which is typically not a huge number. If you were to pick a large amount of bounces, you would still not get an accurate result and the computer won't be able to reasonably calculate the results.

[rhb]

Interesting kid.  Wish I had a neighbor  like that.

For an infinitessimal point source at the center of a perfect reflective sphere, a pulse of light would produce an infinite series of light pulses at the center.  This is something you could do as an experiment *reasonably* easily.  A *very* high speed scope would be required to show the pulses. But you might be able to demonstrate it using the amplitude decay with time.

For a persons head in the middle of a reflective  sphere the result would be like looking into a magnifying mirror.  The reflection from behind them would be blocked.  The way to demonstrate the concepts is with a ruler and compass diagram.  Start with the point source and then ray trace a ball.  For a light source not at the center it gets too messy for me.  You might consider throwing an ellipse back at him as it has two foci.

Have Fun!

[German_EE]

"Interesting kid.  Wish I had a neighbor  like that."

I'm already known as the techy guy around here and a couple of years ago I found him standing on the doorstep with his mother, he'd built up a circuit using batteries and bulbs and he couldn't get it to work (and his parents are technically challenged). In the last couple of years we've covered most of the basic components plus at nine years old he's able to appreciate Ohms Law. This is someone who needs careful nurturing.

He already has some of my old tools and Christmas this year will bring his first soldering iron from his parents and a multimeter from me. We do however have three rules to follow:

1) The ONLY thing he is allowed to plug into the mains supply is the power supply which he got for his birthday, and that is grounded. If he starts messing around with 230V then the lessons stop.

2) Until a few months ago he always came with his mother. She sat in the lounge for a couple of hours reading a magazine whilst we retired to the workshop with the door left open. For obvious reasons I'm being careful here.

3) If in doubt, stop and ask for help. This rule applies to his parents as well if they see something they don't understand and get worried.

[paulca]

[rhb]

That's not a sphere, though it is a very cool device.

It's sad that we live in an age where one needs to be so careful.  I'd probably install some hidden cameras if  I were teaching a child.  Just so an extortion attempt could be trivially rebutted before terminating the relationship.  Fortunately, the  sort of kid who is interested in technology it not likely to try such a stunt.  But it is a concern.  The local library does not have *any* technical books at all.  Not one!  I'm working on correcting that.  I had thought to have kits of parts kids could check out, but concluded that would beat me to death.  A "maker" space would be nice, but raises the aforementioned issues.

[Mr. Scram]

That's not a sphere, though it is a very cool device.

It's sad that we live in an age where one needs to be so careful.  I'd probably install some hidden cameras if  I were teaching a child.  Just so an extortion attempt could be trivially rebutted before terminating the relationship.  Fortunately, the  sort of kid who is interested in technology it not likely to try such a stunt.  But it is a concern.  The local library does not have *any* technical books at all.  Not one!  I'm working on correcting that.  I had thought to have kits of parts kids could check out, but concluded that would beat me to death.  A "maker" space would be nice, but raises the aforementioned issues.

What are you talking about?

[rhb]

[
What are you talking about?

2) Until a few months ago he always came with his mother. She sat in the lounge for a couple of hours reading a magazine whilst we retired to the workshop with the door left open. For obvious reasons I'm being careful here.

This :-(

[IanB]

You're in the center of a very large glass Christmas ball and the inner surface of the thing is a mirror. You turn on your torch, what do you see?

One thing I thought about this is that it sounds rather similar to an integrating sphere, an instrument used for measuring the total light output of a lamp. Could almost be a hobby project to construct one.

[TerraHertz]

One thing I thought about this is that it sounds rather similar to an integrating sphere, an instrument used for measuring the total light output of a lamp. Could almost be a hobby project to construct one.

But an integrating sphere has a matt white inner surface. The mirror sphere is much more raytrace-challenging.

By the way, who has ever looked into a corner-cube reflector?
You see your eye, centered in the cube and reversed. No matter from which angle you look into the corner cube.
Or the camera...

[rhb]

FWIW the 3D image device  is an ellipsoid of revolution.  The illusion is created by truncating the ellipsoid so that the 2nd focus is outside the case.

As for explaining it to the kid, a 2D drawing properly constructed with compass and straight edge will both answer the question and teach him important elements of classical geometry.  Ray trace by hand from a cartoon eye to where the ray falls.  Construct the tangents, perpendiculars and rays using the compass, at least for one or two.

It's a great question, so worthy of effort.  We'd all still live in caves if adults had not properly responded to such questions from children.

As remarked, I'm envious.  A friends' child copped at attitude on me when I was trying to show him how to fix a kinked copper water line while installing a dishwasher for his Mom.  He didn't used to be like that, so I'm hoping he grows back out of it.

[tszaboo]

Simple optics questions. Draw it in 2D and use "ray tracing" to draw the mirror image.

[SparkyFX]

You could start with a planar example and then expand the explanation by changing over to curved surfaces.
Like this:

[Mr. Scram]

This :-(

You shouldn't give in to mania. It'll eat you if you do.

[cdev]

That's great of you. Having somebody encourage me as a kid with some help and a present of a multimeter was instrumental in getting me interested in electronics.

"Interesting kid.  Wish I had a neighbor  like that."

I'm already known as the techy guy around here and a couple of years ago I found him standing on the doorstep with his mother, he'd built up a circuit using batteries and bulbs and he couldn't get it to work (and his parents are technically challenged). In the last couple of years we've covered most of the basic components plus at nine years old he's able to appreciate Ohms Law. This is someone who needs careful nurturing.

He already has some of my old tools and Christmas this year will bring his first soldering iron from his parents and a multimeter from me. We do however have three rules to follow:

1) The ONLY thing he is allowed to plug into the mains supply is the power supply which he got for his birthday, and that is grounded. If he starts messing around with 230V then the lessons stop.

2) Until a few months ago he always came with his mother. She sat in the lounge for a couple of hours reading a magazine whilst we retired to the workshop with the door left open. For obvious reasons I'm being careful here.

3) If in doubt, stop and ask for help. This rule applies to his parents as well if they see something they don't understand and get worried.