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Chapter 26 Refraction
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Refraction Refraction is the bending of light as it passes from one medium into another. Water Air N qw qA refraction Note: the angle of incidence qA in air and the angle of refraction qw in water are each measured with the normal N. The incident and refracted rays lie in the same plane and are reversible.
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Refraction Distorts Vision
Water Air Water Air The eye, believing that light travels in straight lines, sees objects closer to the surface due to refraction. Such distortions are common.
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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
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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? vair = c vG = 2 x 108 m/s Glass Air For glass: n = 1.50 If the medium were water: nW = Then you should show that the velocity in water would be reduced from c to 2.26 x 108 m/s.
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Analogy for Refraction
Sand Pavement Air Glass 3 x 108 m/s 2 x 108 m/s 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.
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Fast to Slow Slow to Fast N N Qi Qi fast slow slow fast Qr refracted ray bends toward N refracted ray bends away from N Qr
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Deriving Snell’s Law Consider two light rays. Velocities are v1 in medium 1 and v2 in med. 2. Medium 1 Medium 2 q1 q2 v1 v1t R v2 v2t q2 Segment R is common hypotenuse to two rgt. triangles. Verify shown angles from geometry.
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Snell’s Law Snell’s Law: q1 q2 Medium 1 Medium 2
The ratio of the sine of the angle of incidence q1 to the sine of the angle of refraction q2 is equal to the ratio of the incident velocity v1 to the refracted velocity v2 . v1 v2 Snell’s Law:
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Example 2: A laser beam in a darkened room strikes the surface of water at an angle of 300. The velocity in water is 2.26 x 108 m/s. What is the angle of refraction? The incident angle is: Air H2O qA 300 qA = 900 – 300 = 600 qW qW = 35.30
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Snell’s Law and Refractive Index
Another form of Snell’s law can be derived from the definition of the index of refraction: Medium 1 q1 q2 Medium 2 Snell’s law for velocities and indices:
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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.
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First find qG inside glass:
Example 3. Light travels through a block of glass, then remerges into air. Find angle of emergence for given information. First find qG inside glass: Glass Air n=1.5 q qG qG 500 qG = 30.70 From geometry, note angle qG same for next interface. qe = 500 Same as entrance angle! Apply to each interface:
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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.) Glass Air n=1 n=1.5 lA lG fA= fG lG < lA
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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.
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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 (nG = 1.5)? nG = 1.5; lA = 632 nm Glass Air n=1.5 q qG 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.
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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.
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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. When the angle reaches a certain maximum, it will be reflected internally. Water Air light 900 The critical angle qc is the limiting angle of incidence in a denser medium that results in an angle of refraction equal to 900. Critical angle qc i = r
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Example 5. Find the critical angle of incidence from water to air.
For critical angle, qA = 900 Water Air qc 900 Critical angle nA = 1.0; nW = 1.33 Critical angle: qc = 48.80 In general, for media where n1 > n2 we find that:
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Total Internal Reflection
reflected ray Qi>Qc glass air If the incident angle is greater than the critical angle, the boundary behaves like a perfect mirror.
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Total Internal Reflection
Qi>Qc FIBER OPTIC CABLE: LIGHT PIPE
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