Optical Path Difference Consider two coherent beams S

Optical Path Difference

Consider two coherent beams S 1 and S 2 where S 1 P is in air and S 2 P is in perspex of refractive index n = 1. 5. We will consider the point P itself to be in air. S 1 P S 2 PERSPEX The geometrical path difference S 1 P - S 2 P is zero. But there will not necessarily be constructive interference at P.

The wavelength inside the perspex is less than in air n = λair. λperspex Hence the waves from S 1 and S 2 may not arrive at P in phase.

The optical path length must be considered not just the geometrical path length. Optical path length = n x geometrical path length Where n is the refractive index. (THIS EQUATION IS NOT GIVEN IN THE EQUATION BOOKLET)

Thus the relationships for constructive and destructive interference must be considered for optical path lengths, S 2 P and S 1 P. For constructive interference (n. S 2 P - S 1 P) = mλ where m is an integer For destructive interference (n. S 2 P - S 1 P) = (m + ½)λ where m is an integer

The optical path difference can be found: Optical path difference = (n 2 – n 1) d Where d is the geometrical distance the waves have travelled. (THIS EQUATION IS NOT GIVEN IN THE EQUATION BOOKLET)

Phase Difference and Optical Path Difference The phase difference is related to the optical path difference: Φ = (2π) x opd λ where λ is the wavelength in a vacuum. Notice that when the optical path difference is a whole number of wavelengths, the phase difference is a multiple of 2π, i. e. the waves are in phase.

Principle of Interference – Division of Amplitude Coherent sources of light can be used to produce interference fringes that can be seen. In order to do this, one ray of light is split into two by reflection and refraction (transmission into the material), then recombined later. This is called interference by division of amplitude.

Incident Refraction (Transmission) Reflection

Notes 1) The amplitude of the incident wave is greater than the amplitudes of the reflected and transmitted waves. 2) In some cases multiple reflections can occur and more than two beams are produced. 3) Extended light sources (e. g. the sun or a fluorescent light tubes) can be used to produce visible interference patterns using this method.