Physics > Wave Optics

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  • A wave front is defined as a surface of constant phase.
  • Huygens' Principle tells us that each point on a wave front is a source of secondary waves, which add up to give the wave front at a later time.

     

  • Huygens' construction tells us that the new wave front is the forward envelope of the secondary waves. When the speed of light is independent of direction, the secondary waves are spherical. The rays are then perpendicular to both the wave fronts and the time of travel is the same measured along any ray. This principle leads to the well known laws of reflection and refraction.
  • Doppler Effect

    o   When the source moves away from the observer the frequency as measured by the source will be smaller. This is known as the Doppler effect.

    o   The fractional change in frequency  is given by  where is the component of the source velocity along the line joining the observer to the source relative to the observer;  is considered positive when the source moves away from the observer.

  •  The principle of superposition of waves applies whenever two or more sources of light illuminate the same point. When we consider the intensity of light due to these sources at the given point, there is an interference term in addition to the sum of the individual intensities. But this term is important only if it has a non-zero average, which occurs only if the sources have the same frequency and a stable phase difference.
  • Young's double slit of separation d gives equally spaced fringes of angular separation. The source, mid-point of the slits, and central bright fringe lie in a straight line. An extended source will destroy the fringes if it subtends angle more than λ/d at the slits.

   

  •  A single slit of width a gives a diffraction pattern with a central maximum. The intensity falls to zero at angles of  etc. with successively weaker secondary maxima in between. Diffraction limits the angular resolution of a telescope to  where D is the diameter. Two stars closer than this give strongly overlapping images. Similarly, a microscope objective subtending angle 2β at the focus, in a medium of refractive index n, will just separate two objects spaced at a distance  which is the resolution limit of a microscope. Diffraction determines the limitations of the concept of light rays. A beam of width a travels a distance , called the Fresnel distance, before it starts to spread out due to diffraction.
  • Natural light, e.g., from the sun is un polarised. This means the electric vector takes all possible directions in the transverse plane, rapidly and randomly, during a measurement. A polaroid transmits only one component (parallel to a special axis). The resulting light is called linearly polarised or plane polarised. When this kind of light is viewed through a second polaroid whose axis turns through 2π, two maxima and minima of intensity are seen. Polarised light can also be produced by reflection at a special angle (called the Brewster angle) and by scattering through  in the earth's atmosphere.

     

Sample Examples

 

Question

What speed should a galaxy move with respect to us so that the sodium line at 589.0 nm is observed at 589.6 nm?

Solution

Since

 

Question

What is the effect on the interference fringes in a Young's double-slit experiment due to each of the following operations?

(a) The screen is moved away from the plane of the slits;

(b) The (monochromatic) source is replaced by another (monochromatic) source of shorter wavelength;

(c) The separation between the two slits is increased;

(d) The source slit is moved closer to the double-slit plane;

(e) The width of the source slit is increased;

(f)The monochromatic source is replaced by a source of white light?

Solution

(a)Angular separation of the fringes remains constant  The actual separation of the fringes increases in proportion to the distance of the screen from the plane of the two slits.

(b) The separation of the fringes (and also angular separation) decreases. See, however, the condition mentioned in (d) below.

(c) The separation of the fringes (and also angular separation) decreases. See, however, the condition mentioned in (d) below.

(d) Let s be the size of the source and S its distance from the plane of the two slits. For interference fringes to be seen the conditions/  should be satisfied; otherwise, interference patterns produced by different parts of the source overlap and no fringes are seen. Thus, as S decreases (i.e., the source slit is brought closer), the interference pattern gets less and less sharp, and when the source is brought too close for this condition to be valid, the fringes disappear. Till this happens, the fringe separation remains fixed.

(e)Same as in (d). As the source slit width increases, fringe pattern gets less and less sharp. When the source slit is so wide that the condition s/S ≤ λ/d is not satisfied, the interference pattern disappears.

(f ) The interference patterns due to different component colours of white light overlap (incoherently). The central bright fringes for different colours are at the same position. Therefore, the central fringe is white. For a point P for which, where  represents the wavelength for the blue colour, the blue component will be absent and the fringe will appear red in colour. Slightly farther away where  where  is the wavelength for the red colour, the fringe will be predominantly blue. Thus, the fringe closest on either side of the central white fringe is red and the farthest will appear blue. After a few fringes, no clear fringe pattern is seen.

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