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Figure 3. Al Hazen’s problem: the case of four points of reflection. Fermat—lenses

Figure 3 Al Hazen’s problem: the case of four points of reflection. Fermat—lenses

Related Figures (12)

Figure 1. Hero’s principle for a curved surface. P Mihas
Figure 1. Hero’s principle for a curved surface. P Mihas
Figure 2. Parabolic mirror. Using the scrollbar time the wavefront moves the scrollbar; ‘change X initial’ moves the incident ray to the left or right of the y axis.
Figure 2. Parabolic mirror. Using the scrollbar time the wavefront moves the scrollbar; ‘change X initial’ moves the incident ray to the left or right of the y axis.
Figure 4. Reflection on an ellipse.
Figure 4. Reflection on an ellipse.
P Mihas Figure 5. Refraction on a convex circular surface with index = 1.6.
P Mihas Figure 5. Refraction on a convex circular surface with index = 1.6.
Figure 6. Extrema in the case of an elliptical surface, with index = 2.2.
Figure 6. Extrema in the case of an elliptical surface, with index = 2.2.
Figure 7. Source of light at the left focus of the ellipse: if n = a/c all rays travel at the same time to a line parallel to y axis 0.
Figure 7. Source of light at the left focus of the ellipse: if n = a/c all rays travel at the same time to a line parallel to y axis 0.
Figure 8. From software ‘lenses’. By clicking on the button ‘SHOW WAVES AND RAYS’ and by a shift click on a point on the screen the rays and wavefronts are displayed. By clicking ‘CUTS OF RAYS’ all the points where the emerging rays cut each other appear. By clicking ‘FERMAT’S PRINCIPLE’ we get rays for the thin lens approximation which are shown on an inset as the times for each ‘ray’ which does not obey exactly the law of refraction.
Figure 8. From software ‘lenses’. By clicking on the button ‘SHOW WAVES AND RAYS’ and by a shift click on a point on the screen the rays and wavefronts are displayed. By clicking ‘CUTS OF RAYS’ all the points where the emerging rays cut each other appear. By clicking ‘FERMAT’S PRINCIPLE’ we get rays for the thin lens approximation which are shown on an inset as the times for each ‘ray’ which does not obey exactly the law of refraction.
P Mihas Figure 9. When a diaphragm is used then most of the ‘rays’ for the thin lens approximation have the same optical length. Also the spread of the cuts is reduced.
P Mihas Figure 9. When a diaphragm is used then most of the ‘rays’ for the thin lens approximation have the same optical length. Also the spread of the cuts is reduced.
Figure 10. A narrow parallel bundle. The rays almost converge to the thin lens approximation focus.
Figure 10. A narrow parallel bundle. The rays almost converge to the thin lens approximation focus.
Figure 12. Rays drawn by using wavefronts.
Figure 12. Rays drawn by using wavefronts.
Figure 11. Wavefronts used in test questions.
Figure 11. Wavefronts used in test questions.
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