Page:Elementary Text-book of Physics (Anthony, 1897).djvu/441

 350. Interference of Light from Two Similar Sources.—It has already been shown that the disturbance propagated to any point from a luminous wave is the algebraic sum of the disturbances propagated from the various elements of the wave. The phenomena due to this composition of light-waves are called interference phenomena.

Let us consider the case in which two elements only are efficient in producing the disturbance. Let $$A$$ and $$B$$ (Fig. 118) represent two elements of the same wave surface separated by the very small distance $$AB.$$ The disturbance at $$m,$$ a point on a distant screen $$mn,$$ parallel with $$AB,$$ due to these two elements, is the resultant of the disturbances due to each separately. The light is supposed to be homogeneous, and its wave length is represented by $$\lambda.$$

When the distance $$mB - mA$$ equals $$\tfrac{1}{2}\lambda$$ or any odd multiple of $$\tfrac{1}{2}\lambda,$$ there will be no disturbance at $$m.$$ Take $$mC = mB,$$ and draw $$BC.$$ $$mCB$$ is an isosceles triangle; but since $$AB$$ is very small compared to $$Osm,$$ the angle at $$C$$ may be taken as a right angle; the triangle $$ACB,$$ therefore, is similar to $$Osm,$$ and we have $$\frac{AB}{AC} = \frac{Om}{sm} = \frac{Os}{sm}$$ very nearly. Represent $$sm$$ by $$x,$$ $$Os$$ by $$c,$$ $$AB$$ by $$b,$$ $$AC$$ by $$n \times \tfrac{1}{2}\lambda,$$ where $$n$$ is any number. Then we have