Magnifying light speed Questions

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Hi Mike,
Curious, what do you think we would see (through the glass) at 99.9% the speed
of light?

I'll just re-state to make sure I have the scenario right: someone ( Bert ) travelling at 99.9% of c towards a mirror, observing his own reflection with a magnifying glass?
A couple of points, then:
- the magnifying glass collects light from the mirror to an image plane - which is stationary in Bert's rest frame. This will distort/enlarge etc what Bert sees according to the optical set up. Light travels at c with respect to this frame and light paths etc can be analysed in the usual way ( ray tracing, waves, even quantum electrodynamics if you like.... ).
- Bert's image of himself is generated from photon's emitted by him which travel ahead, 'hit' the mirror and return. Without loss of generality you can analyse this as a virtual Bert ( VeeBert ), heading toward the mirror plane ( from the other side as Bert ) at speed 99.9% c with respect to that plane. Admittedly there might be a phase issue with reflection, but let's ignore that.
- So take, now, Bert and VeeBert heading toward each other at a speed of 99.9% c with respect to said mirror plane. Convert VeeBert's motion in this frame ( rest frame of mirror ), to Bert's rest frame using Lorentz formulae.
- as pointed out this involves a time correction ( dilation or slowing down of VeeBert's behaviour with respect to Bert ) and the velocity of VeeBert with respect to Bert will be greater than 99.9% of c, but still less than c.
- So Bert looks through his looking glass, sees a delayed and slower version of himself looking back at him through a looking glass!
Phew!
Any holes in that anybody?
Cheers, Mike.

(you guys are so much fun)

Mike, What will you see if you have only a magnifying glass in
front of you?
What will I see through the glass?(No Mirror!)

The further you hold it away, what changes might
occur? (traveling at 99.9% the speed of light)

Remember, I'm a rookie!
Thanks
Ernie S
Team Art Bell
God Bless

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(you guys are so much fun)

You ask fun questions! :-)

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Mike, What will you see if you have only a magnifying glass in
front of you?
What will I see through the glass?(No Mirror!)

The speed of his motion is not really a big issue with respect to the formation of any image within his rest frame. The beauty ( indeed the foundation ) of Relativity is that the speed of light ( in vacuo ) is constant regardless of choice of frame. Bert's motion will of course affect the pattern of arrival of light to his frame. The Lorentz contraction refers only to lengths along the line/vector of relative velocity between source and observer ( be careful how you read that ). Let's not forget good old Doppler shifting which will cause a blueing of light coming from in front of Bert, and a redden-ing from behind, compared to the stationary case. There is also an effect where you need to adjust the aim of an optical device due to relative motion. This was first found a few centuries ago with regard to telescopes - I can't remember who named it - analogous to leaning forwards when running in the rain to catch the drops in the bottom of a long bucket.

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The further you hold it away, what changes might
occur? (traveling at 99.9% the speed of light)

You'd see a different view of whatever tableau was apparent according to the various effects already mentioned. Do you have a special thought, prediction or worry here? Don't be shy .... :-)
Cheers, Mike.

NB. Einstein originally wanted to call his 1906 theory 'Invariant', referring to the constancy of light speed, but settled on 'Relativity' concerning how to relate measurements in different frames. Alas because of other semantic uses of the word 'relative', the effect has been a blossoming of mis-understandings of his ideas.