Go Back   Physics Help Forum > High School and Pre-University Physics Help > Light and Optics

Light and Optics Light and Optics Physics Help Forum

Reply
 
LinkBack Thread Tools Display Modes
Old Sep 14th 2018, 07:46 AM   #1
Junior Member
 
Join Date: Sep 2018
Posts: 2
Shape of refracting surface for focus



So this problem is from the Feynman Lectures V. 1 Ch. 27 Geometrical Optics
272 The focal length of a spherical surface


Now suppose that we have a point at O, at a distance s from the front surface of the glass, and another point O′ at a distance s′ inside the glass, and we desire to arrange the curved surface in such a manner that every ray from O which hits the surface, at any point P, will be bent so as to proceed toward the point O′. For that to be true, we have to shape the surface in such a way that the time it takes for the light to go from O to P, that is, the distance OP divided by the speed of light (the speed here is unity), plus n⋅O′P, which is the time it takes to go from P to O′, is equal to a constant independent of the point P. This condition supplies us with an equation for determining the surface.

The answer is that the surface is a very complicated fourth-degree curve, and the student may entertain himself by trying to calculate it by analytic geometry.
So I decided to entertain myself, to no avail. Does anyone else know how to solve this?

Cheers
Henrik is offline   Reply With Quote
Old Sep 17th 2018, 10:12 AM   #2
Senior Member
 
Woody's Avatar
 
Join Date: Jun 2016
Location: England
Posts: 594
I did once see a picture of one of these lenses,
they must be terrifically awkward to grind
(although perhaps less so now with accurate 3D robotic tools).

As to actually sitting down with the maths,
My idea of "fun" is far lazier than that...
__________________
~\o/~
Woody is offline   Reply With Quote
Old Sep 18th 2018, 03:54 AM   #3
Junior Member
 
Join Date: Sep 2018
Posts: 2
Originally Posted by Woody View Post
I did once see a picture of one of these lenses,
they must be terrifically awkward to grind
(although perhaps less so now with accurate 3D robotic tools).

As to actually sitting down with the maths,
My idea of "fun" is far lazier than that...
Yeah, mine usually is too, but sometimes I get hung up on something.

Anyway, I do think I managed to solve it, I tried posting what I think is the solution, but it seems to have been lost (It said something like pending admin approval).
Henrik is offline   Reply With Quote
Reply

  Physics Help Forum > High School and Pre-University Physics Help > Light and Optics

Tags
feynman, focus, refracting, shape, surface



Thread Tools
Display Modes


Similar Physics Forum Discussions
Thread Thread Starter Forum Replies Last Post
III newton ball shape and cubic shape !? MMM Advanced Mechanics 28 Mar 15th 2015 07:38 AM
How to focus multiple light sources as one? berkbaykal Light and Optics 3 Dec 2nd 2014 10:11 AM
Find Focus and Mirror arya Light and Optics 2 Sep 27th 2012 04:14 AM
Object at Focus of convex lens kenny1999 Light and Optics 3 Oct 8th 2011 06:40 AM
multi-surface problem in refraction at spherical surface. asdfgh Advanced Optics 1 Feb 18th 2011 02:41 AM


Facebook Twitter Google+ RSS Feed