- Email: [email protected]
The limits of the validity of the geometrical law relating to the refraction of light
C U R R E N T TOPICS. The Limits of the Validity of the Geometrical Law Relating to the Refraction of Light. P. FROELICH. (Ann. der Physik., No. 15, t 9 2 I . ) - - L e t a ray of light travel through water upward toward air above the water. The geometrical law governing such a case predicts that this ray will emerge into the air or will be totally reflected back into the water according to the size of the angle of incidence. In fact, the matter is not so simple. A more complete theory indicates and experiment verifies that light really does penetrate into the air even when the geometrical law points to nothing but total reflection. The intensity of the light finding its way into the air diminishes rapidly with the depth of penetration. Let us now consider the case of light originating in air and incident on a surface of water. One ray strikes the surface at right angles and enters with no change of direction. A second ray making an angle of 5 ° with the first meets the surface at a different point, suffers a change of direction and is continued by a ray of light in the water. A ray the direction of which in air makes IO ° with the first encounters the surface of the water at a still different place, there experiences a change in direction greater than that of the second ray and in the water travels in a direction different from that followed in the water by the second ray. As rays farther and farther from the first are traced their points of contact with the water are progressively more distant, the changes of direction at the surface grow greater and greater and the refracted rays within the water make larger and larger angles with a perpendicular to the suface. \Vhen the ray in air just grazes the surface the refracted ray makes its maximum angle with the perpendicular. This angle is designated the critical angle. \Vithin the water let a straight tube be placed in the direction of the first refracted ray. Light from the source in air will come through it and an eye in the water would see the source through the tube. If the tube were shifted to one side and turned so as to lie along the second refracted ray tlle eye could again perceive the source. So long as the direction of the tube when prolonged to meet the surface makes an angle with the perpendicular there that is not greater than the critical angle it is possible by moving the tube about to find a position at which the source can be seen through it. If, however, the angle be made greater than the critical angle, there is no position at which the source can be seen through the tube. At least there should not be were the geometrical law strictly true, but again here theory and experiment unite to show that the angle may in reality be greater than the critical angle and still the source may be seen 887
83 8
CURRENT TOPICS.
[J. F. I.
through the tube, provided that the source be very close to the surface of separation. The purpose of this investigation is to measure the m a x i m u m distance of the source f r o m the surface for different departures of the line of sight beyond the critical angle. Glass was used instead of water. The distance from the source to the surface was measured by a method based on Newton's rings. One set of observations was made with green light of wave-length .000522 mm., for which the critical angle of the glass employed was 38.0 ° . To see the source in air along a line of sight making a n angle with the perpendicular to the surface 2.5 ° greater than the critical angle, the source could not be farther f r o m the surface than 2.5I wave-lengths or .001310 ram. F o r 4 °0 beyond the critical angle the corresponding quantities are .613 wave-lengths or .000320 ram. With the same angles the distances when red light was used are all larger, though equivalent to a smaller number of wave-lengths. G. F. S. O n the V a r i a t i o n of R e s i s t a n c e of S e l e n i u m w i t h T e m p e r a t u r e . SNEHAMOY DATTA. (Phil. Mat]., Sept., I 9 2 I . ) - - T h e curious sensitiveness of selenium to light, which shows itself by an enormous change in electrical resistance when the element is illuminated, has made this substance an important, even an essential, factor in transmitting light effects, such as pictures and photographs, to a distant point. T h e present investigator sets himself the task of finding how far the change of resistance under illumination is due to a change of temperature caused by the absorption of the incident radiation. The resistances of several selenium cells was measured f r o m o ° C. to 17 °0 C. Above the latter temperature sublimation begins. At 217 ° C. is the melting point. F o r one specimen the resistance at zero was 66.0 × IO~ ohms, while at 17°0 C. it was a mere 2 x lO5 ohms. T o determine how largely the change of temperature bulks in the change of resistance consequent upon illumination a cell was measured in the dark and its resistance was found to be 67.0 × lO 5 ohms. It was then exposed to light f r o m which both ultra-violet and infrared wave-lengths had been abstracted. The resistance was then 48.0× lO5 ohms, a decrease of I 9 X IO'~ ohms. A thermo-couple ~howed that the selenium had risen about one degree. F r o m the previous measurements this elevation of temperature would cause a fall in the resistance of .75 × lOS ohms. It thus appears that the heating effect is competent to account for only about one twenty-fifth of the entire change in resistance. Three different types of selenium crystals were obtained. One variety was " primarily non-conducting," a second was only slightly conducting and on this property change of temperature had no effect. T h e third type, appearing red in reflected light, was moderately conducting at the temperature of the room. U p o n warming the red color gradually vanished and at the same time the resistance grew less. This type of crystal may, therefore, well be responsible for the
83 8
CURRENT TOPICS.
[J. F. I.
through the tube, provided that the source be very close to the surface of separation. The purpose of this investigation is to measure the m a x i m u m distance of the source f r o m the surface for different departures of the line of sight beyond the critical angle. Glass was used instead of water. The distance from the source to the surface was measured by a method based on Newton's rings. One set of observations was made with green light of wave-length .000522 mm., for which the critical angle of the glass employed was 38.0 ° . To see the source in air along a line of sight making a n angle with the perpendicular to the surface 2.5 ° greater than the critical angle, the source could not be farther f r o m the surface than 2.5I wave-lengths or .001310 ram. F o r 4 °0 beyond the critical angle the corresponding quantities are .613 wave-lengths or .000320 ram. With the same angles the distances when red light was used are all larger, though equivalent to a smaller number of wave-lengths. G. F. S. O n the V a r i a t i o n of R e s i s t a n c e of S e l e n i u m w i t h T e m p e r a t u r e . SNEHAMOY DATTA. (Phil. Mat]., Sept., I 9 2 I . ) - - T h e curious sensitiveness of selenium to light, which shows itself by an enormous change in electrical resistance when the element is illuminated, has made this substance an important, even an essential, factor in transmitting light effects, such as pictures and photographs, to a distant point. T h e present investigator sets himself the task of finding how far the change of resistance under illumination is due to a change of temperature caused by the absorption of the incident radiation. The resistances of several selenium cells was measured f r o m o ° C. to 17 °0 C. Above the latter temperature sublimation begins. At 217 ° C. is the melting point. F o r one specimen the resistance at zero was 66.0 × IO~ ohms, while at 17°0 C. it was a mere 2 x lO5 ohms. T o determine how largely the change of temperature bulks in the change of resistance consequent upon illumination a cell was measured in the dark and its resistance was found to be 67.0 × lO 5 ohms. It was then exposed to light f r o m which both ultra-violet and infrared wave-lengths had been abstracted. The resistance was then 48.0× lO5 ohms, a decrease of I 9 X IO'~ ohms. A thermo-couple ~howed that the selenium had risen about one degree. F r o m the previous measurements this elevation of temperature would cause a fall in the resistance of .75 × lOS ohms. It thus appears that the heating effect is competent to account for only about one twenty-fifth of the entire change in resistance. Three different types of selenium crystals were obtained. One variety was " primarily non-conducting," a second was only slightly conducting and on this property change of temperature had no effect. T h e third type, appearing red in reflected light, was moderately conducting at the temperature of the room. U p o n warming the red color gradually vanished and at the same time the resistance grew less. This type of crystal may, therefore, well be responsible for the