L04 Vergence_DMS_2024_StudentNotes.pdf

1/10/24 OPTM 4101 Principles of Optics & Vergence – the introduction Danuta Sampson, Discipline of Optometry, SAH...

1/10/24 OPTM 4101 Principles of Optics & Vergence – the introduction Danuta Sampson, Discipline of Optometry, SAH [email protected] 1 Acknowledgement of country The University of Western Australia acknowledges that its campus is situated on Noongar land, and that Noongar people remain the spiritual and cultural custodians of their land, and continue to practise their values, languages, beliefs and knowledge. Artist: Dr Richard Barry Walley OAM 2 1  1/10/24 Learning objectives 1. Explain what is the vergence. 2. Explain how sign convention work and if the distance should be positive or negative. 3. Understand and explain how refractive index and curvature of a surface impact the vergence. 4. Be able to calculate vergence. 3 3 Key terms related to light Credit: S. Strong: Introduction to visual optics. A light approach. 4 4 2  1/10/24 Key terms related to light Radius !! < !" Sphere 1 Sphere 2 r1 r2 Curvature Sphere 1 l rl > Curvature Sphere 2 l r2 Credit: S. Strong: Introduction to visual optics. A light approach. 5 5 Key terms related to light Wavefronts Wavefronts + light rays A pencil – selection of a few rays close together. A beam – a group of pencils originating Credit: S. Strong: Introduction to visual optics. A light approach. from all of the points on a light source. 6 6 3  1/10/24 Vergence (L) all directed towards a point without crossing. focus point. ⑳ · Credit: S. Strong: Introduction to visual optics. A light approach. 7 7 Vergence (L) Reciprocal of the radius of curvature of the wavefront. · A B C have same vergence. Measured in Dioptre (D) = 1/m light source , $%&'%()% = + = 23450/! !(./0/!) rA rB rC Wavefronts Parallel Wavefront Vergence = O ve 1 Wavefront Vergence - Diverging : 67897:;7 ?@=87 1/rB > 1/rC rC 9 9 Diverging wavefronts and rays Light propagation - Vergence movement Divergence implies the point away from a Curvature of wavefronts decreases as light & propagates → DIVERGENCE < , $%&'%()% = + = =“−” −! Radius measured from the wavefront to the point source 10 10 5  1/10/24 Converging wavefronts and rays Light propagation + Vergence Convergence implies a movement Awards a point , $%&'%()% = + = =“+” +! Radius measured from the wavefront to the point source Converging wavefronts: concentric circles increasing their curvature (vergence) as light propagates, until forming a point image at their centre. 11 11 Vergence and propagation The value of the vergence changes as the wavefront propagates. closer to the source , the vergence is more negative. : The distance from the source is shorter. 12 Credit: S. Strong: Introduction to visual optics. A light approach. 12 6  1/10/24 Plane wavefronts: Image at optical infinity Plane Wavefronts Radius ~ Infinity Credit: https://en.wikipedia.org/wiki/Wavefront Curvature ~ Zero 13 13 Plane wavefronts: Image at optical infinity really far away from the source. Observer is Optical 6-10 meters. system Credit: Figures 2.7 Keating 14 14 7  1/10/24 Sign convention for wavefronts/vergence from always assume that light travels Direction of light left to the right. Convergent optical system Point source/Object Image point Radius is measured from the surface of the wavefront Principal axis along the axis to the centre of Diverging wavefronts Converging wavefronts curvature. Object Space Image Space Distance: - ve Distance: + ve 15 15 Vergence calculation Light diverging from point source Direction of light = , += 23450/! !(./0/!) Vergence L at a position 50 cm to the right of the point source is: - 50CM = 0 5M. L= - 2 D 5 = 16 16 8  1/10/24 Vergence calculation Light diverging from point source Direction of light , += 23450/! !(./0/!) Vergence L at a position 50 cm to the right of the point source is: L= 1/-0.5m = ‐ 2 D = light is diverging 2 D at that position 17 - - 17 Vergence calculation Light converging towards image point => Direction of light 50cm = 0. 5 m Vergence L at a position 50 cm to the left the image point is: Liv5 = 2 D Light is converging 2D at that position. 18 18 9  1/10/24 Vergence calculation Light converging towards image point Direction of light Vergence L at a position 50 cm to the left the image point is: L= 1/+0.5m = +2 D = light is converging 2 D at that position 19 19 Vergence calculation Light converging towards image point Even if certain length Direction of light expressions are not reported/available in meters, before engaging in any calculations that involve vergence or optical power, distances should -- be Vergence L at a position 50 cm to the left the image point is: converted to meters. - # L= 1/+0.5m = +2 D = light is converging 2 D at that position 20 20 10  1/10/24 Generalized, Equivalent or “Reduced” Vergence E* /I FRIP* AF , When light travels in a medium other than vacuum, the speed of light decreases and wavelength shortens. - - - 21 21 Generalized, Equivalent or “Reduced” Vergence Vergence (n = 1) Reduced Vergence (n>1) 1 1 1 : : : 1.33 K= = = = −1 M K= K= = = = −1.33 M air 1 = I : 8 L −1 8 8 L −1 Vacuum: n = 1 Water: n = 1.33 Same distance, but rays more spread out (more divergent) 22 22 11  1/10/24 Calculation of the vergence at different points Light propagation agint Bi - Ve has. vergence calculated at a point that Vacuum: n = 1 +30 cm - 60 cm direction traveled with the stream , along the of light propagation is downstream. ,. converging to B -> - + 90 cm A B C The vergence calculated at a point that has to 1 ! A: K# = = +3.3 M Downstream vergence (air): !! = +0.3Q 1−%&! travel against the stream , in a direction ! 1 Downstream vergence (other medium): !! = against the light of propagation is upsteam C: K$ = = −1.67 M % , −0.6Q 1−'&! 23 23 Summary Vergence is an expression of the wavefront curvature. Vergence describes light as converging or diverging. The sign of the vergence depends on geometry with respect to the direction of light propagation. Vergence is positive in converging rays. Vergence is negative in diverging rays. Vergence is zero, in parallel (flat) rays. The unit of vergence is the Dioptre (D), which is the reciprocal of the meter. The longer the distance, the less the vergence. The larger the vergence, the shorter the distance to focus. 24 24 12  1/10/24 Question Calculate the vergence for plane wavefront. 25 Credit: S. Strong: Introduction to visual optics. A light approach. 25 References and Resources 1. Hecht, E. (2017). Optics. Pearson. 2. Strong, S. (2023). Introduction to visual optics: a light approach. Elsevier. 3. Schwartz, S.H. (2002). Geometrical and visual optics: A clinical introduction. McGraw-Hill Education. 4. Bennett, A.G. and Rabbett, R.B. (2007). Clinical visual optics. Butterworth-Heinemann. 26 26 13