Boundary between two media n 1 n 2 q i q t Incident stream of photons Reflected

# Boundary between two media n 1 n 2 q i q t incident

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Boundary between two media n 1 n 2 q i q t Incident stream of photons Reflected stream of photons Refracted or transmitted stream of photons n 1 < n 2 q i = Incident angle q r = Reflection angle q t = Refraction or transmission angle n 1 = Refractive index Refraction/Transmission: n 1 Sin q i = n 2 Sin q t Snell’s Law Reflection: q i = q r Normal Reflection Coefficient : R = (n 2 – n 1 )/ (n 1 + n 2 ) Reflectance : R 1 = R 2 q r Electric field vs light intensity
When photons meet a boundary 6 Boundary between two media n 1 n 2 q i q t Incident stream of photons Reflected stream of photons Refracted or transmitted stream of photons n 1 > n 2 q i = Incident angle q r = Reflection angle q t = Refraction or transmission angle n 1 = Refractive index Refraction/Transmission: n 1 Sin q i = n 2 Sin q t Snell’s Law Normal q r Why is n 1 in this example called the slow medium and n 2 the fast medium?
Refraction 7 External Refraction : When the ray is incident from the medium of smaller refractive index, and the refracted ray bends away from the boundary Internal Refraction : If the incident ray is in medium of higher refractive index, and the refracted ray bends towards the boundary
Total Internal Reflection 8 For internal refraction n 1 > n 2 , the angle of refraction is greater than the angle of incidence, q t > q i So that as q i increases, q t reaches 90 0 This occurs when q i = q c (Critical angle) q c = sin -1 n 2 /n 1 when q i > q c , Snell’s law cannot be satisfied and refraction does not occur. The incident ray is totally reflected as if the surface were a perfect mirror. This is known as total internal reflection.
Total Internal Reflection 9 Just under the water's surface, If the water is calm, its surface appears mirror-like.
Transmission through a parallel sided slab 10 n 2 q i q t q t q i n 1 d 1 d 2 n 2 n 2 < n 1 Relevance: Allowance needs to be made in optical systems e.g.. bar code. A stream of photons entering a parallel sided block exits it at a point displaced a distance d from where it entered. a d 1 = a tan q t d 2 = a [tan q i – tan q t ] q t < q c
Transmission in a parallel sided slab 11 n 0 q i q t q t q t > q c n 1 n 2 n 2 < n 0 < n 1 q t q t q i q i A stream of photons entering a parallel sided block exiting it on the same side as it enters does so at a point displaced a distance d from where it entered. Note that at the n 1 and n 2 boundary the transmission angle exceeds the critical angle and therefore the photons are totally internally reflected . a d = 2a tan q t d
q t q t The guided ray in parallel slab 12 n 0 q i q t q t n 1 q t q t n 2 n 2 n 0 q t q t Note relevance to optical fibres . Light propagates in the parallel slab through total internal reflection. Note relevance to optical fibres. n 2 < n 0 < n 1 q t > q c
Simple illustration of total internal reflection 13
Dispersion 14 White light consists of a mixture of different colours (wavelengths).

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