كتاب المناظر (The Optics of Ibn al-Haytham, Books I-III)

[48] As for the accidental lights that appear on opaque bodies, the lights radiating from them on the bodies that confront them may also be subjected to an accurate experiment in the following way. Let the experimenter employ a pure white wall which can be exposed to daylight and to sunlight and moonlight; I 39a | and opposite, near and parallel to this wall let another wall stand. And behind each of the walls let there be a chamber into which the light may enter only through a door. Let the experimenter then take a block of wood not less than one cubit in length, breadth and depth. Let him smooth its surfaces, making them as plane and parallel as possible, and let its edges be straight and parallel. He should then draw, in the middle of two facing surfaces, two straight and parallel lines, each parallel to two edges of the surface in which it is drawn. Then, from the ends of each one of these lines, let him cut off two equal segments, neither of them more than the breadth of two digits. Two points are thus marked on each of the two lines.

[49] About the two points on one of the lines let him draw two equal circles, each with a diameter equal to the breadth of one digit of a fair size. Then, about one of the two points on the other line, he should draw a circle equal I 39b | to each of the two former circles, then divide the line between the centre of the circle and the other point assumed on this line into two parts — such that the ratio of the smaller part to the greater is as the ratio of the thickness of the wooden block to the interval between the two walls. (He may determine this interval with the help of a straight rod, making sure that it lies perpendicularly to both walls.) The line having been divided in that ratio, let the greater part corresponding to the interval between the walls lie next to the circle drawn on this line. When this division has been properly made, there should be drawn about the dividing point a circle equal to each of the previous circles. Then, componendo a mathematical rule of proportion whereby, if a/b = c/d, then (a+b)/b = (c+d)/d, the ratio of the line between the centres of the two far circles on the first, undivided line, to the line between the centres of the near circles on the divided line, will be as the ratio of the thickness of the wooden block plus the interval between the walls, to this interval itself.

I 40a | [50] The experimenter should bore two holes in the wooden block. One of these should be from the outermost of the two near circles to the outermost and opposite circle of the two circles on the other surface. Let the hole be circular and cylindrical, and let its circumference coincide with that of the two facing circles. This hole, then, will be at right angles to the two parallel surfaces. Let the other hole extend from the circle at the dividing point on the line to the other, similarly outermost circle of the two far circles in the other surface. And let the circumference of the hole coincide with that of the two circles. This hole will then be inclined to the two parallel surfaces.

[51] When these holes have been properly made, let him make in the wall opposite the white wall a square hole as wide as the wooden block. Let him

I 40b mount the block in this hole with the surface having the two near circles facing outwards. He should make sure, while mounting the wooden block, that its surface parallels that of the white wall. | Further, the distance of its surface from the white wall should be exactly equal to the inter-mural interval according to which the line has been divided. When the wooden block has been precisely positioned, he should plug any gaps that may be left round it, and firmly fix it in place. If the thickness of the wall exceeds that of the block he should obliquely remove the excess from within the chamber so as to give the remainder of the hole a conical shape. But it would be better to make the thickness of the block equal to that of the wall from the outset.

[52] When the wooden block has been perfectly mounted, let the experimenter take a perfectly straight rod equal in thickness to the width of the hole in the block. Better still, he should obtain a straight rod thicker than the width of the hole, and then turn it in a lathe to make it exactly and uniformly equal in thickness to the hole's width. Having properly prepared this rod, let him sharpen one end of it I 41a | into the shape of a cone with the point of its vertex appearing as the extremity of the axis of the rod. He should then insert the rod into the perpendicular hole and move it along the hole until the sharpened end meets the surface of the white wall. When this happens let him mark the point of contact. This point will then be on a straight line with the axis of the perpendicular hole. This done, let him take the rod out of the hole.

[53] The experimenter should now enter the chamber into which this hole gives, place one eye at the circumference of the perpendicular hole, and look at the white wall, searching for the limit of what he can perceive of that wall, and for the farthest perceptible place from the point assumed on the wall to be in a straight line with the axis of the perpendicular hole. He should instruct someone to mark this place with a point. The experimenter should then turn his eye round the circumference of the hole, looking from every side of it at the wall, and searching for the farthest perceptible place I 41b | on the wall from the assumed point. He will find that the farthest perceptible distances from the assumed point opposite the centre of the hole are always equal — for this is a characteristic property of round holes.

[54] With the first point on the white wall as centre and with a radius equal to the farthest distance that his eye has perceived on the wall, let the experimenter draw a circle.

[55] Then, again placing his eye at the hole's circumference and looking towards the drawn circle, he will perceive the circle's circumference and nothing beyond it. Let him move his eye round the hole's circumference; if he sees nothing outside it, then the circle will have been properly placed. If, however, his eye perceives something outside the circumference, or if he fails to perceive the circumference from some or all positions, then the circle will