REFRACTION Refraction is the bending of light as

REFRACTION Refraction is the bending of light as it passes from one medium into another. Note: the angle of incidence q. A in air and the angle of refraction q. A in water are each measured with the normal N. Air q. A qw N Water refraction The incident and refracted rays lie in the same plane and are reversible.

REFRACTION DISTORTS VISION Air Water The eye, believing that light travels in straight lines, sees objects closer to the surface due to refraction. Such distortions are common.

THE INDEX OF REFRACTION The index of refraction for a material is the ratio of the velocity of light in a vacuum (3 x 108 m/s) to the velocity through the material. Index of refraction c v Examples: Air n= 1; glass n = 1. 5; Water n = 1. 33

EXAMPLE 1. LIGHT TRAVELS FROM AIR (N = 1) INTO GLASS, WHERE ITS VELOCITY REDUCES TO ONLY 2 X 108 M/S. WHAT IS THE INDEX OF REFRACTION FOR GLASS? Air vair = c Glass v. G = 2 x 108 m/s For glass: n = 1. 50 If the medium were water: n. W = 1. 33. Then you should show that the velocity in water would be reduced from c to 2. 26 x 108 m/s.

ANALOGY FOR REFRACTION 3 x 108 m/s Pavement Air Glass 2 x 108 m/s Sand vs < vp 3 x 108 m/s Light bends into glass then returns along original path much as a rolling axle would when encountering a strip of mud.

SNELL’S LAW Medium 1 v 1 q 2 v 2 Medium 2 Snell’s Law: The ratio of the sine of the angle of incidence q 1 to the sine of the angle of refraction q 2 is equal to the ratio of the incident velocity v 1 to the refracted velocity v 2.

EXAMPLE 2: A LASER BEAM IN A DARKENED ROOM 0. STRIKES THE SURFACE OF WATER AT AN ANGLE OF 30 8 M/S. WHAT IS THE VELOCITY IN WATER IS 2. 26 X 10 THE ANGLE OF REFRACTION? 300 Air q. A H 2 O The incident angle is: q. A = 900 – 300 = 600 q. W = 35. 30

SNELL’S LAW AND REFRACTIVE INDEX Another form of Snell’s law can be derived from the definition of the index of refraction: q 1 Medium 1 q 2 Medium 2 Snell’s law for velocities and indices:

A SIMPLIFIED FORM OF THE LAW Since the indices of refraction for many common substances are usually available, Snell’s law is often written in the following manner: The product of the index of refraction and the sine of the angle is the same in the refracted medium as for the incident medium.

EXAMPLE 3. LIGHT TRAVELS THROUGH A BLOCK OF GLASS, THEN REMERGES INTO AIR. FIND ANGLE OF EMERGENCE FOR GIVEN INFORMATION. First find q. G inside glass: Air Glass q. G 500 q q. G n=1. 5 Air From geometry, note angle q. G same for next interface. q. G = 30. 70 Apply to qe each = 500 interface: Same as entrance angle!

WAVELENGTH AND REFRACTION The energy of light is determined by the frequency of the EM waves, which remains constant as light passes into and out of a medium. (Recall v = fl. ) Air l. A f. A= f G Glass n=1. 5 l. G < l A

THE MANY FORMS OF SNELL’S LAW: Refraction is affected by the index of refraction, the velocity, and the wavelength. In general: Snell’s Law: All the ratios are equal. It is helpful to recognize that only the index n differs in the ratio order.

EXAMPLE 4: A HELIUM NEON LASER EMITS A BEAM OF WAVELENGTH 632 NM IN AIR (NA = 1). WHAT IS THE WAVELENGTH INSIDE A SLAB OF GLASS N ( G = 1. 5)? n. G = 1. 5; Air Glass q. G q q. G n=1. 5 l. A = 632 nm q Air Note that the light, if seen inside the glass, would be blue. Of course it still appears red because it returns to air before striking the eye.

DISPERSION BY A PRISM Red Orange Yellow Green Blue Indigo Violet Dispersion is the separation of white light into its various spectral components. The colors are refracted at different angles due to the different indexes of refraction.

TOTAL INTERNAL REFLECTION When light passes at an angle from a medium of higher index to one of lower index, the emerging ray bends away from the normal. Air 900 qc i=r Critical light angle Water When the angle reaches a certain maximum, it will be reflected internally. The critical angle qc is the limiting angle of incidence in a denser medium that results in an angle of refraction equal to 900.

EXAMPLE 5. FIND THE CRITICAL ANGLE OF INCIDENCE FROM WATER TO AIR. For critical angle, q. A = 900 Critical n. A = 1. 0; n. W = 1. 33 angle Air 900 qc Critical angle: qc = 48. 80 In general, for media where n 1 > n 2 we find that: Water

SUMMARY c = 3 x 108 m/s Medium n Index of refraction v Refraction is affected by the index of refraction, the velocity, and the wavelength. In general: Snell’s Law:

SUMMARY (CONT. ) The critical angle qc is the limiting angle of incidence in a denser medium that results in an angle of refraction equal to 900. In general, for media where n 1 > n 2 we find that: Critical angle n 2 qc 900 n 1 > n 2