Two identical small isotropic sources and each radiate a radiant flux of at a single…

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Wave propagation and light in media · Wave propagation and light in media

Optics and Photonics, Ch Harmonic waves, phasors and group velocity

Problem

Two identical small isotropic sources

S_1

and

S_2

each radiate a radiant flux of

0.60\ \mathrm{W}

at a single vacuum wavelength of

500\ \mathrm{nm}

, and they are maintained exactly in phase with each other. Both lie on the same straight line through a point

P

in air of index

1.000

, with

S_1

1.50\ \mathrm{m}

from

P

and

S_2

3.00\ \mathrm{m}

from

P

, on the same side. At

P

the two fields are parallel and add as scalars; absorption in the air is ignored, and each wave is spherical with its amplitude falling as

1/r

. ((a)) Find the irradiance at

P

from each source alone, and the ratio of the field amplitude of the wave from

S_2

to that from

S_1

P

. ((b)) Express the geometric path difference between the two routes as a number of vacuum wavelengths, and hence find the total irradiance at

P

. ((c)) A plate of glass of index

1.500

and thickness

0.500\ \mathrm{\mu m}

is now inserted in the beam from

S_1

, replacing an equal thickness of air. Find the extra optical path difference it introduces, the new phase difference, and the total irradiance at

P