File Name: light reflection and refraction class 10 numericals creator.zip
Question 1. A Polaroid is placed in the path of the emergent ray at point P and rotated about an axis passing through the centre and perpendicular to the plane of the polaroid. The reflected light is plane polarised represented by arrows.
- NCERT Exemplar Class 12 Physics Chapter 10 Wave Optics
- Light- Reflection and Refraction-NCERT Solutions
- Mirror Formula
- Mirror Formula
This process is called reflection of light. Spherical mirrors are of two types. They are concave mirror and convex mirror.
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NCERT Exemplar Class 12 Physics Chapter 10 Wave Optics
We theoretically show that owing to the optical feedback effect which originates from the wave reflections at the air-dielectric interface, the proposed half-wave plate exhibits a broadened and flattened response when comparing to the case where the feedback effect is absent.
Moreover, our theoretical analysis also reveals that the half-wave plate has an interesting feature of broad angular response. Metasurface 1 , 2 refers to a general class of planar structures that consist of subwavelength scale elements called as the unit cells.
It has a close analogy to and also represents a much enriched extension of the frequency selective surface originally proposed for microwave electronics 3. One of the most fascinating features of the metasurface is its electromagnetic response that can be engineered almost at will. Taking advantage of this feature, a variety of intriguing wave phenomenon such as the generalized Snell law for reflection and refraction 4 and the high resolution light focusing for plane waves 5 have been demonstrated using ultrathin optical structures.
Some other important engineering outcomes enabled by the development of the metasurface may include the polarization manipulators 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , and in particular the linear polarization converters. For linear polarization converters, it is well known that they can be separated into the transmitting cases 16 , 17 , 18 , 19 , 20 , 21 and the reflecting cases 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , Note that viewed from a practical perspective, the development of the reflective type linear polarization converter encounters two demanding issues that need to be carefully addressed.
The first issue is the spectral bandwidth issue, which can be solved, e. The second issue is the incidence angle issue since in order to conveniently separate the output beam from the input beam, the half-wave plate should be capable to accept incident angles as large as a few tens of degrees. We emphasize that in general, these two issues of the reflective type half-wave plate may not be resolved simultaneously.
In this article, we propose and demonstrate a kind of reflective type linear polarization converter half-wave plate that can possess broad spectral and angular bandwidths at the same time. We start our device design by first considering a simple version of the reflective type half-wave plate that consists of a metal grating placed on top of a grounded metal surface.
We next show that the spectral bandwidth of the half-wave plate can be broadened by enclosing the metal grating with a dielectric slab, which introduces a beneficial optical feedback effect due to the wave reflections occurring at the air-dielectric interface. Moreover, it is also analytically proven that the proposed device has a feature of broad angular bandwidth. Based on these features, we propose and demonstrate that the conceived device can function as a broadband freely tunable linear polarization rotator that can work with an incident angle as large as 45 degrees.
It consists of a metal grating and a grounded metal surface. When the pitch and duty cycle of the metal grating are properly arranged, the metal grating allows waves with polarization perpendicular to the grating wires to be efficiently transmitted, while makes waves with polarization parallel to the grating wires to be efficiently reflected.
In other words, the metal grating and the grounded metal surface can be viewed as virtual reflectors for cases of parallel and perpendicular polarizations respectively. We note that because the polarization related phase difference is determined by the separation between the two virtual reflectors, which is a fixed value upon the completion of the device fabrication, the bandwidth of the half-wave plate depicted by Fig.
Illustrations on the design and operating principle of the proposed device. Note that at the desired wavelength of interest where the quarter-wavelength condition is strictly satisfied, the reflected wave would have a polarization exactly aligned along the direction 45 degrees to the grating wires cross-polarized due to the perfect polarization conversion effect of the ideal half-wave plate.
Referring to Fig. We emphasize that the existence of the co-polarized component of the reflected beam, i. By eliminating it with the help of certain means, the bandwidth of the half-wave plate will be broadened.
Based on the above arguments, we propose an optical feedback method to eliminate the co-polarized component of the reflected beam and consequently increase the bandwidth of the half-wave plate.
Here the idea is to feed the co-polarized component of the reflected beam back to the grounded-grating structure and reutilize the polarization conversion effect of such a structure for suppressions. It consists of a metal grating embedded inside a dielectric slab and placed on top of a grounded metal surface. Note that our theoretical analysis presented in the Methods section indicates that for optimized performance the metal grating should be positioned at the middle plane of the dielectric slab, of which the thickness is half of the wavelength of interest.
Comparing to the case of Fig. The addition of the dielectric slab creates an air-dielectric interface, which introduces an optical feedback effect by reflecting the co-polarized component back to the device kernel, i. The co-polarized component of the reflected beam then undergoes further rounds of polarization conversion processes and in an intuitive sense, may be cancelled out with appropriate arrangements.
We unitize a multiple-reflection model to determine the optimal condition for the cancellation of the co-polarized component of the reflected beam. As being illustrated by Fig. The first channel is the direct reflection channel since when the incident wave impinges onto the air-dielectric interface, it will be partially reflected due to the mismatch of the air and dielectric impedances.
Such a channel is denoted by letter A in Fig. The reflected wave produced in this channel is completely co-polarized and has an amplitude coefficient of. Upon the reflection, the incident wave will continue to propagate into the dielectric slab and be reflected back by the grounded-grating structure. The reflected beam from the grounded-grating structure has two components, with one being co-polarized and the other being cross-polarized.
These two polarization components will subsequently undergo multiple reflections between the air-dielectric interface and the grounded-grating structure, and create the second and third channels for the co-polarized components. Such two channels are denoted by letters B and C in Fig.
We remark that for the multiple-reflection processes, reflections from the grounded-grating structure will alter the polarization state while reflections from the air-dielectric interface will preserve the polarization state.
It therefore takes four reflections for the trapped beam to complete a cycle, as being illustrated by the five arrows drawn with different colors in the dashed box B and C of Fig. The two channels of B and C are coupled to the external space through wave transmissions at the air-dielectric interface. With some manipulations, the amplitude coefficients of the co-polarized components from these two channels read as. Summing up contributions from these three channels, the overall amplitude coefficient for the co-polarized component of the reflected beam reads as.
Note that in deriving the above result, higher order polarization conversion processes have been neglected. If these processes are taken into considerations, it can be shown that the exact value of the permittivity of the dielectric slab is 2 and the cancellation is at the level of second order accuracy. Please refer to the Methods section for a rigorous proof. The much increased bandwidths for these devices are attributed to the multiple reflections occurring at the interfaces of the dielectrics.
It is confirmed numerically that this arrangement allows the wire grating to be highly transparent for incident waves with perpendicular polarizations but highly reflective for incident waves with parallel polarizations. Note that in our simulations carried out with the CST microwave studio , we have assumed that the metal has a conductivity and a thickness of 5. Three different cases where the dielectric slabs have permittivities of 2, 2.
In comparison, Fig. Comparing Fig. We remark that Fig. This is in an agreement with our theoretical prediction presented in the Methods section.
When the permittivity of the dielectric slab varies from 2 to 2. The good tolerance on the dielectric permittivity of the proposed device greatly alleviates the restrictions for the selection of the slab materials. Numerical results for the proposed half-wave plate under normal incidence. For comparison purpose, c and d sketch the response curves obtained for the narrowband design case where the dielectric slabs is absent.
Note that in fabricating the tested device, we first print a metallic grating onto a grounded dielectric slab, and then attach a second dielectric slab with the same thickness on top of it.
We use copper for the metal and F4BK for the dielectric. The copper structure has a thickness of 0. Such a permittivity is expected to lead to a good device performance according to the simulation results obtained previously. The fabricated samples are mounted onto an absorbing screen and are tested using a microwave network analyzer connected to a transmitting antenna and a receiving antenna both are placed vertically.
This allows normal incidence condition to be approximately achieved in the measurements. By arranging the fabricated device in manners where the grating wires are vertically oriented and horizontally oriented, two sets of data for the reflection phases are obtained.
Their difference is plotted by the red curve shown in Fig. The measured result is in a good agreement with the numerical one shown by the blue curve. The results are sketched by the solid curves in Fig. The good agreement between the experimental and numerical data shown in Fig. Experimental and numerical results for the proposed half-wave plate operating under quasi-normal incidence.
Note that the incident angle is 5 degrees. We emphasize that in order to make the proposed device practically useful, in addition to the requirement of the broad spectral bandwidth, it is also preferred that the device can work with incident angles as large as a few tens of degrees, since larger incident angles provide greater convenience for the experiments.
It is thus necessary to study the device performance under cases of oblique incidences. To this end, referring to the inset of Fig. With such an arrangement being emulated in the numerical simulations the permittivity of the dielectric slab is 2. The obtained results are sketched by the curves drawn with red, yellow and blue colors in Fig. It can be seen that other than a shift of the central working frequency, the performance of the half-wave plate does not suffer any deterioration even if the incident angle is as large as 60 degrees.
Moreover, we have also calculated the phase difference of the reflected beams between cases where the polarizations of the input beams are parallel and perpendicular to the grating wires under oblique incidences.
The results are presented in Fig. It is hence numerically demonstrated that the proposed half-wave plate is insensitive to the incident angles except a shift of the central working frequency. Such a numerical result is in agreement with the theoretical prediction drawn in the Methods section.
Numerical results for the proposed half-wave plate under oblique incidence. The insect in a shows the oblique incidence situation under consideration.
Motivated by the broad spectral and angular responses of the conceived half-wave plate, we propose to function it as a polarization converter that can rotate the linear polarization of the output beam by arbitrary angles. The non-ideal operation of the half-wave plate will yield some reflection components being perpendicular to the polarization converted beam referred as the polarization unconverted beam and denoted as E unc.
To evaluate how much portion of E i is converted to E con and how much portion of E i is left as E unc , experimental measurements are carried out. By measuring r h and r v respectively and with the help of Eqs 8 and 9 , the amplitude coefficients for the polarization converted and unconverted components are obtained. Their results are summarized in Fig. It can be seen that under the condition of 45 degrees incidence, the proposed device can freely rotate the linear polarization of the reflected beam, while leaving very low polarization unconverted residues in a broadband manner.
Light- Reflection and Refraction-NCERT Solutions
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Light is an electromagnetic wave. As shown below, an electromagnetic wave is a transverse wave consisting of mutually perpendicular oscillating electric and magnetic fields. Questions pertaining to reflection and refraction If youre seeing this message, it means were having trouble loading external resources on our website. If youre behind a web filter, please make sure that the domains. Light, Shadows And Reflections. Answer Given, radius of curvature 32 cm Focal Length radius of curvature 2 32 2 16 cm A ray of light is the straight line along which the light traveled and a bundle of light rays is called a beam of light. Laws of Reflection of light.
Define the principal focus of a concave mirror.
Лифт, соединяющий шифровалку с основным зданием, получал питание из главного комплекса, и оно действовало, несмотря на отключение питания шифровалки. Стратмору, разумеется, это было хорошо известно, но даже когда Сьюзан порывалась уйти через главный выход, он не обмолвился об этом ни единым словом. Он не мог пока ее отпустить - время еще не пришло. И размышлял о том, что должен ей сказать, чтобы убедить остаться.
Беккера очень удивило, что это кольцо с какой-то невразумительной надписью представляет собой такую важность. Однако Стратмор ничего не объяснил, а Беккер не решился спросить. АНБ, - подумал. - НБ - это, конечно, не болтай. Вот такое агентство. На другой стороне авениды Изабеллы он сразу же увидел клинику с изображенным на крыше обычным красным крестом на белом поле. С того момента как полицейский доставил сюда канадца, прошло уже несколько часов.
Велел ему сегодня не приходить. Он ничего не сказал о том, что поменялся с тобой дежурством. У Чатрукьяна ком застрял в горле. Он молчал. - Ну ладно, - вздохнул Стратмор. - Похоже, вышла какая-то путаница. - Он положил руку на плечо Чатрукьяна и проводил его к двери.