Properties of Stationary Waves

When two simple harmonic waves of same amplitude, frequency and time period travel in opposite directions in a straight line, the resultant wave obtained is called a stationary or a standing wave.

Properties of stationary waves:

1) In these waves, nodes and anti nodes are formed alternately.
   Nodes are positions where particles are at their mean positions having maximum strain.
   Anti nodes are positions where the particles vibrate with maximum amplitude having minimum strain.

2) The medium is split into segments and all particles of same segment vibrate in phase. The particles in one segment have a phase difference of '𝜫 ' with the particles in neighboring segment.

3) Condensations and rarefractions do not travel forward as in progressive wave but they appear and disappear alternately at same place.

4) As condensations and rarefractions do not travel forward there is no transfer of energy.

5) The distance between two adjacent nodes is 'ƛ/2' and also the distance between two adjacent antinodes is 'ƛ/4'. Between the two nodes there is anti node and vice versa.

6) The general appearance of wave can be represented by a sine curve but it reduces to straight line twice in each time period.

REFLECTION, REFRACTION AT PLANE SURFACES

LAWS OF REFLECTION

 The angle of incidence is equal to angle of reflection.

 The incident ray, Normal and Reflected ray ray all lie in one plane. 

PROPERTIES OF IMAGE FORMED BY PLANE MIRROR

1.  The image formed by a plane mirror is "virtual", "erect" and laterally reversed.
2.  The size of image is equal to size of object.
3.  The image is as far behind the mirror as the source is in front of it.
4.  When the plane mirror is rotated through certain angle, the reflected ray turns through double the angle.
5.  When two plane mirrors are kept facing each other at an angle '𝛳 ' and an object is placed between them, multiple images of the object are formed as a result of multiple successive reflections.

            a) If (360/𝛳) is "even", then no. of images is given by n = (360/𝛳)-1

            b)  If (360/𝛳) is "odd", then following two situations arise 

     

                   i) If object lies symmetrically, then n = (360/𝛳)-1

                  ii)  If object lies unsymmetrically, then n = 360/𝛳

            c) When two plane mirrors are placed parallel to each other, then  

                 n = (360/0) = ∞ (infinite no. of images)

Note:- 

I) The point object for a mirror is a point from which the rays incident on mirror actually diverge or towards which the incident rays appear to converge.

II) An optical image is a point where rays of light either intersect or appear to do so.

REFRACTION OF LIGHT

The Refracted ray bends towards the Normal when the second medium is denser than first medium and vice versa.

The deviation 'D' suffered by refracted ray is given by D =  i-r

LAWS OF REFRACTION

1. The Incident ray, the Refracted ray and the Normal to surface separating two media lie in one plane.

2. Snells Law: For any media, the ratio of sine of angle of incidence to sine of angle of refraction is a constant for a light beam of particular wavelength.

sini/sinr = 𝜇2/𝜇1 = constant

Refractive index 𝜇 = velocity of light in vacuum / velocity of light in medium