4.1 Single-slit diffraction

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By the end of this section, you will be able to:
• Explain the phenomenon of diffraction and the conditions under which it is observed
• Describe diffraction through a single slit

After passing through a narrow aperture (opening), a wave propagating in a specific direction tends to spread out. For example, sound waves that enter a room through an open door can be heard even if the listener is in a part of the room where the geometry of ray propagation dictates that there should only be silence. Similarly, ocean waves passing through an opening in a breakwater can spread throughout the bay inside. ( [link] ). The spreading and bending of sound and ocean waves are two examples of diffraction    , which is the bending of a wave around the edges of an opening or an obstacle—a phenomenon exhibited by all types of waves.

The diffraction of sound waves is apparent to us because wavelengths in the audible region are approximately the same size as the objects they encounter, a condition that must be satisfied if diffraction effects are to be observed easily. Since the wavelengths of visible light range from approximately 390 to 770 nm, most objects do not diffract light significantly. However, situations do occur in which apertures are small enough that the diffraction of light is observable. For example, if you place your middle and index fingers close together and look through the opening at a light bulb, you can see a rather clear diffraction pattern, consisting of light and dark lines running parallel to your fingers.

Diffraction through a single slit

Light passing through a single slit forms a diffraction pattern somewhat different from those formed by double slits or diffraction gratings, which we discussed in the chapter on interference. [link] shows a single-slit diffraction pattern . Note that the central maximum is larger than maxima on either side and that the intensity decreases rapidly on either side. In contrast, a diffraction grating ( Diffraction Gratings ) produces evenly spaced lines that dim slowly on either side of the center.

The analysis of single-slit diffraction is illustrated in [link] . Here, the light arrives at the slit, illuminating it uniformly and is in phase across its width. We then consider light propagating onwards from different parts of the same slit. According to Huygens’s principle    , every part of the wave front in the slit emits wavelets, as we discussed in The Nature of Light . These are like rays that start out in phase and head in all directions. (Each ray is perpendicular to the wave front of a wavelet.) Assuming the screen is very far away compared with the size of the slit, rays heading toward a common destination are nearly parallel. When they travel straight ahead, as in part (a) of the figure, they remain in phase, and we observe a central maximum. However, when rays travel at an angle $\theta$ relative to the original direction of the beam, each ray travels a different distance to a common location, and they can arrive in or out of phase. In part (b), the ray from the bottom travels a distance of one wavelength $\lambda$ farther than the ray from the top. Thus, a ray from the center travels a distance $\lambda \text{/}2$ less than the one at the bottom edge of the slit, arrives out of phase, and interferes destructively. A ray from slightly above the center and one from slightly above the bottom also cancel one another. In fact, each ray from the slit interferes destructively with another ray. In other words, a pair-wise cancellation of all rays results in a dark minimum in intensity at this angle. By symmetry, another minimum occurs at the same angle to the right of the incident direction (toward the bottom of the figure) of the light.

what is an atom
All matter is composed of two sets of three dimensions. The first set (1,2,3) decay with a positive charge. The second set (4,5,6) decay with a negative charge. As they decay, they create space (7 8,9) dimensions.
John
Two sets of (1,2,3,4,5,6) dimensions create a proton, a neutron, and an electron. This is the primordial atom.
John
A 10kg mass lift to a height of 24m and release. what is the total energy of the system
mechanics is that branch of physical and mathatics that
E=Mgh=10*10*24=2400J
what is the difference between a molecule and atom
Atoms are single neutral particles. Molecules are neutral particles made of two or more atoms bonded together.
Manfred
what I'd dynamic propulsion
A body quadruples its momentum when its speed doubles.What was the initial speed in units of c.i.e..what was u/c ?
what is enthalpy?
a thermodynamic quantity equivalent to the total heat content of a system
RAMLA
proparty of tharmo dainamic
bloch
What is the meaning of Nuclear Fission?
what do you mean by dynamics single particles
عند قذف جسم إلى أعلى بسرعة إبتدائية فإنه سيصل إلى ارتفاع معين (أقصى ارتفاع) ثم يعود هابطاً نحو سطح الأرض .   إذا قُذِفَ جسم إلى أعلى ووجد أن سرعته 18 م / ث عندما قطع 1/4 المسافة التي تمثل أقصى ارتفاع سيصله فالمطلوب إيجاد السرعة التي قُذِف بها بالمتر / ث . إن هذه السرعة هي واحدة من الإجابات التالية
what is light
light is a kind of radiation That stimulates sight brightness a source of illumination.
kenneth
Electromagnet radiation creates space 7th, 8th, and 9th dimensions at the rate of c.
John
That is the reason that the speed of light is constant.
John
This creation of new space is "Dark Energy".
John
The first two sets of three dimensions, 1 through 6, are "Dark Matter".
John
As matter decays into luminous matter, a proton, a neutron, and an electron creat deuterium.
John
There are three sets of three protons, 9.
John
There are three sets of three neutrons, 9.
John
A free neutron decays into a proton, an electron, and a neutrino.
John
There are three sets of five neutrinoes, 15.
John
Neutrinoes are two dimensional.
John
A positron is composed of the first three dimensions.
John
An electron is composed of the second three dimensions.
John
What is photoelectric
light energy (photons) through semiconduction of N-P junction into electrical via excitation of silicon purified and cristalized into wafers with partially contaminated silicon to allow this N-P function to operate.
Michael
i.e. Solar pannel.
Michael
Photoelectric emission is the emission of electrons on a metal surface due to incident rays reflected on it
Benita
If you lie on a beach looking at the water with your head tipped slightly sideways, your polarized sunglasses do not work very well.Why not?
it has everything to do with the angle the UV sunlight strikes your sunglasses.
Jallal
this is known as optical physics. it describes how visible light, ultraviolet light and infrared light interact when they come into contact with physical matter. usually the photons or light upon interaction result in either reflection refraction diffraction or interference of the light.
Jallal
I hope I'm clear if I'm not please tell me to clarify further or rephrase
Jallal
what is bohrs model for hydrogen atom
hi
Tr
Hello
Youte
Hi
Nwangwu-ike
hi
Siddiquee
hi
Omar
helo
Mcjoi
what is the value of speed of light
1.79×10_¹⁹ km per hour
Swagatika
3×10^8
Benita
what r dwarf planet