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LENSES

In this software we use ray tracing to show the formation of an image point. There is an option for comparing the real behavior of rays with the thin lens model (option ray). By clicking waves and rays wave fronts and the corresponding rays are depicted. By clicking waves in time, the wave fronts are seen to be moving and they seem to be slowed down inside the lens for the case of n>1 and speeding up for the case of n<1, where n is the ratio of wave speed outside the lens to the wave speed inside the lens. Also a thick lens model is introduced. The students can see that the thin lens model is adequate in many cases

INTRODUCTORY PAGE

In the introductory form the following buttons are presented

--------Ibn Sahl lens ----------------------------SPHERICAL LENS- HUYGENS LENS-- FERMAT'S PRINCIPLE

WHAT CAN BE FOUND IN EACH BUTTON?

The first two buttons refer to two "perfect" lenses devellloped by IBN Sahl in the 9th century Ibn Sahl discovered the hyperbolic lenses by which he theorized a perfect focusing of parallel beams.
The button SPHERICAL LENSES is the main part of the software BACK TO THE TOP
The button HUYGENS LENS presents Huygens method of calculating the shape of a "perfect" lens that focuses exactluy to one point. Ibn Sahl's lens can be considered as a special case of Huygens' method GOTO SPECIAL FEATURES TO EXAMINE THE HUYGENS LENS BACK TO THE TOP
FERMAT'S PRINCIPLE introduce a "spherical lens" in which the user can move the point on the right side of the lens to obtain a minimum time path from source. BACK TO THE TOP

SPECIAL MENU ITEMS FOR SPHERICAL LENSES

AKTINA RAY: EXAMINES THE BEHAVIOUR OF A SINGLE RAY IT COMPARES IT'S BEHAVIOUR TO THE RAY THAT CORRESPONDS TO THE THIN LENS OR THICK LENS APPROXIMATION. A SPECIAL BUTTON SHOWS THE MAIN RAYS BACK TO THE TOP
PARALLE (//) BUNDLE: SHOWS THE BEHAVIOUR OF A PARALLEL BUNDLE, RAYS ARE SHOWN, OR WAVE FRONTS OR WAVE FRONTS WITH RAYS
// WAVES: SHOWS THE WAVES MOVING TO THE RIGHT, AS THEY PASS THROUGH THE LENS THEIR SPEED IS EITHER REDUCED OR INCREASED. IT IS INCREASED IF n= c(outside)/c(inside)<`1 and IS DECREASED WHEN n= c(outside)/c(inside)>`1 TO SEE THE WAVES THE BUTTON "SHOW ONLY WAVES' MUST BE PRESSED BACK TO THE TOP
SINGLE POINT SOURCE: IT PRODUCES A BUNDLE OF RAYS. IF THE BUTTON "ONLY WAVES' IS PRESSED THEN WAVE FRONTS MOVING THROUGH THE LENS ARE PRODUCED BACK TO THE TOP
FERMAT;S PRINCIPLE: IT SHOWS AT FITHG SCREEN A FORM THAT DEPICTS THE TIME NEEDED FOR THE LIGHT TO REACH THE IMAGE POINT ACCORDINT TO THE LENS TO THE THIN MODEL APPROXIMATION, FROM THE POINTS OF THE LENS . THE FORM HAS A 'ZOOM' OPTION: IT SHOWS MORE CLEARLY THE TIME DIFFERENCE. THIS DIFFERENC DIMINISHES AS THE DIAPHRAGM IS DRAGED TO MAKE THE BUNDLE MOR NARROW AND THE SOURCE IS NEARER TO THE HORIZONTAL AXIS. CUTS OF RAYS: IT CAN BE USED WHEN THE BUTTON 'RAYS AND WAVES' IS PRESSED. IT SHOWS THE POINTS WHERE THE RAYS CUT EACH OTHER. THIS SHOWS THAT THE RAYS ACTUALLY DO NOT CUT EACH OTHER AT A SINGLE POINT THE CROSS IS THE VARIATION IN THE POSITION IN THE HORIZONTAL AND VERTICAL DIRECTION BACK TO THE TOP
THE OPTION 'PRINT' PERMITS A PRINTOUT TO BE PRODUCED AND THIS CAN BE GIVEN TO STUDENTS . FOR EXAMPLE WHEN 'ONLY WAVES' IS PRESSED IT GIVES A PRINT OUT OF WAVES	HUYGENS LENS: IT GIVES THE HUYGEN'S LENS CONSTRUCTION

SPECIAL FEATURES OF HUYGENS; LENS

HUYGENS LENS HAS SOME SCROLL BARS BACK TO THE TOP OTHER FEATURES ARE WAVE FRONTS NEXT ARE EXAMINED THE SCROLLBARS THE OPTION HYPERBOLIC PRODUCES A HYPERBOLIC LENS THE OPTION PRINT GIVES A PRINTOUT
BY PRESING THE OPTION 'WAVE FRONTS', THE IMAGE ON THE RIGHT IS PRODUCED BACK TO THE TOP
BY MOVING THE SCROLL BAR 'F' THE DISTANCE OF THE F CAN BE CHANGED BACK TO THE TOP
THE SCROLL BAR AB CHANGES THE WIDHT OF THE LESN BACK TO THE TOP
THE SOURCE POINT CAN BE MOVED BY THE SCROLL BAR 'INITIAL POINT' BACK TO THE TOP
BY PRESSIN 'HYPERBOLA' THE FRONT SURFACE IS A HYPERBOLIC INSTEAD OF CIRCLULAR: BY PRESSING on the n SCROLLBAR THE SHAPE CHANGES: FOR BIGGER n IT BECOMS FLATER BY PRESSING 'ZOOM +" OR "ZOOM -" THE SCALE CHANGES AND THE FOCUS OF THE HYPERBOLA CAN BE SEEN. IF THE INITIAL POINT IS ON THE FOCUS THEN THE RIGHT SIDE OF THE HYPERBOLA BECOMES A STRAIGHT LINE: THIS IS THE CASE OF IBN SAHL'S LENS BACK TO THE TOP
THE MENU 'PRINT FOR CONSTRUCTION' GIVES THE PICTURE OF A PARTIALLY CONSTRUCTED LENS IN THE PRINTOUT THE NUMBER OF WAVE FRONTS 9ACTULLY A MULTIPLE OF THEM) IS SHOWN. ON THE BOTTOM IS SEEN THE POSITION OF THE SOURCE, THE STUDENT CAN CALCULATE THE DISTANCE OF SOURCE FROM THE LENS IN 'WAVE LENGTHS' IN THE UPPER PART OF THE SCREEN IS SHOWN THE WIDTH OF THE SCREEN IN ''WAVE LENGTHS", AND THE OTHER 'RULER' SHOWS THE DISTANCE OF THE FOCUS POINTS FROM THE MIDDLE OF THE BACK SIDE. BACK TO THE TOP
The teacher by using a special software distributed a diagram with the in which were drawn the wave fronts before the lens (the 14th front touches the lens) and inside the lens with the 10th front considered as crossing the optical axis at the back end of the lens. The students had to construct a circle with radius =11 λ so that the total optical length along the axis of the lens was 35 λ. This circle touches the back of the lens. Then they had to add some circles which represent converging wave fronts towards the pint F. Then the students draw the circle with radius 12λ which cut the 9th wave front inside the lens in two points which determine two points at which the lens end in the back. Then they continue with the circles with radiuses 13λ, 14λ, 15λ and 16λ. They cut the 8th, 7th, 6th, and the 5th wave fronts. The last cut is very near the spherical surface. Then they draw a smooth curve between the points which represents the back surface of the curve. In figure are typical student’s results.
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