Diffraction is the slight bending of light as it passes around the edges of an object. The amount of bending depends on the relative size of the wavelength of light to the size of the opening. If the opening is much larger than the light’s wavelength, the bending will be almost unnoticeable. However, if the two are closer in size or equal, the amount of bending is considerable, and easily seen with the naked eye.
Single Slit Diffraction:
Waves diffract when they encounter obstacles. Why does this happen? If we apply Huygens principles it becomes clear. Think about a wavefront impinging on a barrier with a slit in it, only the points on the wavefront that move into the slit can continue emitting forward moving waves- but because a lot of the wavefront has been blocked by the barrier, the points on the edges of the hole emit waves that bend round the edges.
Before the wavefront strikes the barrier the wavefront generates another forward moving wavefront (applying Huygens Principle). Once the barrier blocks most of the wavefront, the forward moving wavefront bends around the slit because the secondary waves they would need to interfere with the primary waves to create a straight wavefront.
Diffraction Pattern:
Each point on the wavefront moving through the slit acts like a point source. Think about some of the effects of this if we analyze what happens when two point sources are close together and emit wavefront with the same wavelength and frequency. These two point sources represent the point sources on the two edges of the slit and we can call the source A and source B.
Each point source emits wavefront from the edge of the slit. In the diagram we show a series of wave fronts emitted from each point. The black lines show peaks in the waves emitted by the point sources and the gray lines represent troughs. We label the place where constructive interference (peak meets a peak or trough meets a trough) takes place with a solid diamond and places where destructive interference (trough meets a peak) takes place with a hollow diamond. When the wave fronts hit a barrier there will be places on the barrier where constructive interference takes place and places where destructive interference happens.
The measurable effect of the constructive or destructive interference at a barrier depends on what type of waves we are dealing with. If we were dealing with sound waves, then it would be very noisy at points along the barrier where the constructive interference is taking place and quiet where the destructive interference is taking place.
Effect of Slit Width and Wavelength on Diffraction Patterns
The extent to which the diffracted wave passing through the slit spreads out depends on the width of the slit and the wavelength of the waves. The narrower the slit, the more diffraction there is and the shorter the wavelength the less diffraction there is. The degree to which diffraction occurs is:
Difference between Interference and Diffraction
In interference and diffraction, light energy is redistributed. If it reduces in one region, producing a dark fringe, it increases in another region, producing a bright fringe. There is no gain or loss of energy, which is consistent with the principle of conservation of energy.
Resolving Power of Optical Instruments
Telescope:
The angular resolution of the telescope is determined by the objective of the telescope. The stars which are not resolved in the image produced by the objective cannot be resolved by any further magnification produced by the eyepiece. The primary purpose of the eyepiece is to provide magnification of the image produced by the objective. The radius of the central bright region is approximately given by
where f is the focal length of the lens and 2a is the diameter of the circular aperture or the diameter of the lens, whichever is smaller.
Thus ∆θ will be small if the diameter of the objective is large. This implies that the telescope will have better resolving power if a is large. It is for this reason that for better resolution, a telescope must have a large diameter objective.
Microscope:
The resolving power of the microscope is given by the reciprocal of the minimum separation of two points seen as distinct.
The resolving power can be increased by choosing a medium of higher refractive index. Usually oil having a refractive index close to that of the objective glass is used. Such an arrangement is called an ‘oil immersion objective’. It is not possible to make sinβ larger than unity. Thus, we see that the resolving power of a microscope is basically determined by the wavelength of the light used.