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Solution for the question - spherical aberration in spherical mirrors is a defect which is due todependence of focal length f on angle of incidence  q  as shown

Spherical aberration in spherical mirrors is a defect which is -Turito

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Most materials have the refractive index, n &gt; 1 So, when a light ray from air enters a naturally occurring material, then by Snell’s <img src="data:image/png;base64,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" class="Wirisformula" alt="text law,  end text fraction numerator sin invisible function application theta subscript 1 end subscript over denominator sin invisible function application theta subscript 2 end subscript end fraction equals fraction numerator n subscript 1 end subscript over denominator n subscript 2 end subscript end fraction comma" width="134" height="44" style="vertical-align:-17px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mtext»law, «/mtext»«mfrac»«mrow»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«msub»«mrow»«mi»θ«/mi»«/mrow»«mrow»«mn»1«/mn»«/mrow»«/msub»«/mrow»«/mrow»«/mrow»«mrow»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«msub»«mrow»«mi»θ«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msub»«/mrow»«/mrow»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«msub»«mrow»«mi»n«/mi»«/mrow»«mrow»«mn»1«/mn»«/mrow»«/msub»«/mrow»«mrow»«msub»«mrow»«mi»n«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msub»«/mrow»«/mfrac»«mo»,«/mo»«/math»'/> it is understood that the refracted ray bends towards the normal But it never emerges on the same side of the normal as the incident ray According to electromagnetism, the refractive index of the medium is given by the relation, <img src="data:image/png;base64,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" class="Wirisformula" alt="n equals open parentheses fraction numerator c over denominator V end fraction close parentheses equals plus-or-minus square root of epsilon subscript r end subscript mu subscript r end subscript end root" width="142" height="38" style="vertical-align:-14px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»n«/mi»«mo»=«/mo»«mfenced separators=¨|¨»«mrow»«mfrac»«mrow»«mi»c«/mi»«/mrow»«mrow»«mi»V«/mi»«/mrow»«/mfrac»«/mrow»«/mfenced»«mo»=«/mo»«mo»±«/mo»«msqrt»«msub»«mrow»«mi»ε«/mi»«/mrow»«mrow»«mi»r«/mi»«/mrow»«/msub»«msub»«mrow»«mi»μ«/mi»«/mrow»«mrow»«mi»r«/mi»«/mrow»«/msub»«/msqrt»«/math»'/>, where c is the speed of the electromagnetic waves in vacuum, v its speed in the medium, er and mr are negative, one must choose the negative root of n Such negative refractive index materials can now be artificially prepared and are called metamaterials They exhibit signficantly different optical behaviour, without violating any physical laws Since n is negative, it results in a change in the direction of propagation of the refracted light However, similar to normal materials, the frequency of light remains unchanged upon refraction even in metamaterials For light incident from air on a meta-material, the appropriate ray diagrams

Solution for the question - most materials have the refractive index, n > 1 so, when a light ray fromair enters a naturally occurring material, then by snells a

Most materials have the refractive index, n > 1 so, when a ligh-Turito

Let <img src="data:image/png;base64,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" class="Wirisformula" alt="A equals open square brackets table row 1 2 cell negative 3 end cell row 0 1 2 row 0 0 1 end table close square brackets" width="110" height="70" style="vertical-align:-30px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»A«/mi»«mo»=«/mo»«mfenced open=¨[¨ close=¨]¨ separators=¨|¨»«mrow»«mtable»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»0«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»0«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mrow»«/mfenced»«/math»'/> Þ |A| = 1 <img src="data:image/png;base64,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" class="Wirisformula" alt="a d j left parenthesis A right parenthesis equals open square brackets table row 1 2 cell negative 1 end cell row cell negative 2 end cell 1 1 row 7 cell negative 2 end cell 1 end table close square brackets to the power of T end exponent" width="180" height="71" style="vertical-align:-30px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»a«/mi»«mi»d«/mi»«mi»j«/mi»«mo»(«/mo»«mi»A«/mi»«mo»)«/mo»«mo»=«/mo»«msup»«mrow»«mfenced open=¨[¨ close=¨]¨ separators=¨|¨»«mrow»«mtable»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»7«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mrow»«/mfenced»«/mrow»«mrow»«mi»T«/mi»«/mrow»«/msup»«/math»'/>. Hence, <img src="data:image/png;base64,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" class="Wirisformula" alt="A to the power of negative 1 end exponent equals fraction numerator a d j left parenthesis A right parenthesis over denominator vertical line A vertical line end fraction" width="103" height="41" style="vertical-align:-16px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«msup»«mrow»«mi»A«/mi»«/mrow»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«mo»=«/mo»«mfrac»«mrow»«mi»a«/mi»«mi»d«/mi»«mi»j«/mi»«mo»(«/mo»«mi»A«/mi»«mo»)«/mo»«/mrow»«mrow»«mo»|«/mo»«mi»A«/mi»«mo»|«/mo»«/mrow»«/mfrac»«/math»'/> Þ <img src="data:image/png;base64,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" class="Wirisformula" alt="A to the power of negative 1 end exponent equals open square brackets table row 1 cell negative 2 end cell 7 row 2 1 cell negative 2 end cell row cell negative 1 end cell 1 1 end table close square brackets" width="155" height="70" style="vertical-align:-30px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«msup»«mrow»«mi»A«/mi»«/mrow»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«mo»=«/mo»«mfenced open=¨[¨ close=¨]¨ separators=¨|¨»«mrow»«mtable»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«mtd»«mn»7«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»2«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mrow»«/mfenced»«/math»'/> . Hence, element <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACUAAAANCAYAAAAuYadYAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAMlJREFUeNpjYKA/cATibUD8DYh/APEtIJ4AxMIMAwj2A3EQELMhiRkA8Q6GQQg+YROsB+L/WHA5HRykBMQ3iFEoCcQHgVgUh/x/IjAhIA7EidB05UVIsSAQ7wZiaRqFDLrjCwhp4ADiTUCsQ4doA3k+AIhPArE9PoXLgdiWDN+SE30wwAN1GFYwDYh9Bij3/cAmWAnE8QPkID1oYkcBkXTK+gzQHB0KxCxAzAQt4e9jC5APONIEGw0cBUqvW6DR9QNawg9UkiEeAADmyz0VWtytPgAAAF10RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+ejwvbWk+PG1vPj08L21vPjxtbj4zPC9tbj48L21hdGg+7lhjEwAAAABJRU5ErkJggg==" class="Wirisformula" alt="z equals 3" width="37" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»z«/mi»«mo»=«/mo»«mn»3«/mn»«/math»'/>.

The element in the first row and third column of the inverse of the matrix <img src="data:image/png;base64,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" class="Wirisformula" alt="open square brackets table row 1 2 cell negative 3 end cell row 0 1 2 row 0 0 1 end table close square brackets" width="81" height="70" style="vertical-align:-30px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfenced open=¨[¨ close=¨]¨ separators=¨|¨»«mrow»«mtable»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»0«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»0«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mrow»«/mfenced»«/math»'/>is

Solution for the question - the element in the first row and third column of the inverse of the matrix[[1,2,-3],[0,1,2],[0,0,1]] is 7

The element in the first row and third column of the inverse of-Turito

If A and B are non-singular square matrices of same order, then <img src="data:image/png;base64,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" class="Wirisformula" alt="a d j left parenthesis A B right parenthesis" width="56" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»a«/mi»«mi»d«/mi»«mi»j«/mi»«mo»(«/mo»«mi»A«/mi»«mi»B«/mi»«mo»)«/mo»«/math»'/> is equal to

Solution for the question - if _a_ and _b_ are non-singular square matrices of same order, then adj(ab)is equal to (adja^(-1))(adjb^(-1))   (adjb^(-1))(adja^(-1))

If _a_ and _b_ are non-singular square matrices of same order, -Turito

<img src="data:image/png;base64,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" class="Wirisformula" alt="vertical line A d j A vertical line equals vertical line A vertical line to the power of n minus 1 end exponent equals d to the power of n minus 1 end exponent" width="177" height="20" style="vertical-align:-4px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»|«/mo»«mi»A«/mi»«mi»d«/mi»«mi»j«/mi»«mi»A«/mi»«mo»|«/mo»«mo»=«/mo»«mo»|«/mo»«mi»A«/mi»«msup»«mrow»«mo»|«/mo»«/mrow»«mrow»«mi»n«/mi»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«mo»=«/mo»«msup»«mrow»«mi»d«/mi»«/mrow»«mrow»«mi»n«/mi»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«/math»'/>.

If d is the determinant of a square matrix A of order n, then the determinant of its adjoint is

Solution for the question - if d is the determinant of a square matrix a of order n, then thedeterminant of its adjoint is o   d^(n+1)   d^(n-1)

If d is the determinant of a square matrix a of order n, then t-Turito

<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIwAAAARCAYAAAAPOESjAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAA25JREFUeNrtWDFoVEEQ/RxySAjCISGEQ64RSWFxYBHEIgQsJFgEQeQQkRC4wkIshBQSRMTGSkKaEIKIhMBxiIjYBDkkiI2IWIgEUoikCMJhEcIhwjkL78Myzu7O/3f/Y+APPLjbmd2ZfX/+7OyPon/lF+FmJMshoRQllx7hD+E7YZfwijCRYO20fvMWbZwau5DNnRTzh87xacJXwrZD9yUFiWbeZzb2kPBUuXZav3mLNk6NXcjmGuE34ViC+ZlwPEfYIDwjnBF0mwOsacsVNuZbO63fvEUb56D7qeDhbmEtrY9MOL5PWCTMEB45dLGY8vWAsI9sN1Wk5lnTFpOQlwI2Gp1WNLEaP3cJ46h+pkR3CbeF9UYJyzi+zXHbJqwo49Tsx2ezSmigbVhJMD8TjltW1r736Iy8BmkVPJCWI+PjcWNTJ6wL52/L87b4dFrRxNpCcphkmYZdFQkxwpKvQ5jH7xMgvK+MU7Mfl8157CVCYu8mmJ8JxzsgKc66i5bum6VrwAmvGrOONfvAAassko2E6gDJoo3VxNAU5psqc9L6v+R4G3eUcWrsJBvTr3wknLLGPhEmlfOHznEJZTiWGoiVdB1kuy3vhDJfQpIYKSMBP7D+yLaJBJIOB6wumlhdMUj+f+BI8nHn4/gg4XPgR6Ytpm24pZifCcdTINeWLZDDdfwK5grIzHvLxq4THgds7BLcGfJVV4p1yuGH+68j2SLl/DR2ks0kqgmXaXyiCM3PhOMGu+pGaKyagu4ns7vg2FADPYstNwhrAb8aXZx8/cC+NLG6/PBxc7t7niLOJHaSzbbnKOHXa2l+JhybpnCBjZWRmcvsfN8jHGfnetux5jwbW0eQPr+2runQnUVjHkoYTayuGPj4nNAPRUiipiJhJD5CPs26Tzz2m6wfkzjLhOMXjqZ1Dff+WfbhbRXlvYZvKm8ca8ZN7hjhKq60ZYVfIy8dugp6oaoiYTSxumLg4yP4sFnH/3O4tex59uDiw2cTrzUB7kc99gssoaS9ZMJxl72JdgnvC7p7eNuWoNsXrmZdq3T28DZUlX59urbVyPYVDyoUq8uPND6OB9ADoTOBPbj44CgLPk3MlwNrVnED8sWcB8eJZSynL6qL6IOiATaTV6xHVYbB8X8jrje0kIJj9eYKKTguEqbguNjMkef4L1dIOOZfOoAPAAABA3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5OPC9taT48bWk+YTwvbWk+PG1pPkI8L21pPjxtc3ViPjxtaT5IPC9taT48bW4+NDwvbW4+PC9tc3ViPjxtbz4mI3hBMDs8L21vPjxtaT5hPC9taT48bWk+bjwvbWk+PG1pPmQ8L21pPjxtbz4mI3hBMDs8L21vPjxtaT5MPC9taT48bWk+aTwvbWk+PG1pPkE8L21pPjxtaT5sPC9taT48bXN1Yj48bWk+SDwvbWk+PG1uPjQ8L21uPjwvbXN1Yj48L21hdGg++NsKlwAAAABJRU5ErkJggg==" class="Wirisformula" alt="N a B H subscript 4 space a n d space L i A l H subscript 4" width="140" height="17" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»N«/mi»«mi»a«/mi»«mi»B«/mi»«msub»«mi»H«/mi»«mn»4«/mn»«/msub»«mo»§#160;«/mo»«mi»a«/mi»«mi»n«/mi»«mi»d«/mi»«mo»§#160;«/mo»«mi»L«/mi»«mi»i«/mi»«mi»A«/mi»«mi»l«/mi»«msub»«mi»H«/mi»«mn»4«/mn»«/msub»«/math»'/> attacks only carbonyl group and reduce it into alcohol group. They do not attack on double bond. <img src="data:image/png;base64,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" alt="" /><img 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" 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<img src="data:image/png;base64,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" class="Wirisformula" alt="C subscript 6 H subscript 5 minus C H equals C H C H O not stretchy rightwards arrow with X on top C subscript 6 H subscript 5 C H equals C H C H subscript 2 O H" width="340" height="25" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»C«/mi»«mn»6«/mn»«/msub»«msub»«mi»H«/mi»«mn»5«/mn»«/msub»«mo»§#8722;«/mo»«mi»C«/mi»«mi»H«/mi»«mo»=«/mo»«mi»C«/mi»«mi»H«/mi»«mi»C«/mi»«mi»H«/mi»«mi»O«/mi»«mover accent=¨true¨»«mo stretchy=¨false¨»§#8594;«/mo»«mi»X«/mi»«/mover»«msub»«mi»C«/mi»«mn»6«/mn»«/msub»«msub»«mi»H«/mi»«mn»5«/mn»«/msub»«mi»C«/mi»«mi»H«/mi»«mo»=«/mo»«mi»C«/mi»«mi»H«/mi»«mi»C«/mi»«msub»«mi»H«/mi»«mn»2«/mn»«/msub»«mi»O«/mi»«mi»H«/mi»«/math»'/>  In the above sequence X can be

Solution for the question - c_(6)h_(5)-ch=chchorarrc_(6)h_(5)ch=chch_(2)oh in the above sequence_x_ can be both (a) and (b)k_(2)cr_(2)o_(7)//h^(+) nabh_(4)

C_(6)h_(5)-ch=chchorarrc_(6)h_(5)ch=chch_(2)oh in the above-Turito

Solution for the question - a ray of light traveling in air is incident at grazing angle ( i 90)on a long rectangular slab of a transparent medium of thickness

A ray of light traveling in air is incident at grazing angle (-Turito

Solution for the question - a point object o is placed along x-axis an equi-convex thin lens(mu_(g)=1.5) of focal length f=20cm in air is placed so that its pri

A point object o is placed along x-axis an equi-convex th-Turito

Solution for the question - an object is placed 20 cm in front of a plano convex lens of focallength 15 cm the plane surface of the lens is silvered the image w

An object is placed 20 cm in front of a plano convex lens of-Turito

Solution for the question - two thin convex lenses of focal lengths f1 and f2 are separated by ahorizontal distance d (where {:d < f_(1),d < f_(2)) and their ce

Two thin convex lenses of focal lengths f1 and f2 are separated-Turito

For a convex lens, if real image is formed the graph between (u + v) andu or v is as follows

Solution for the question - for a convex lens, if real image is formed the graph between (u + v) anduor v is as follows

For a convex lens, if real image is formed the graph between (u-Turito

Solution for the question - a ray op of monochromatic light is incident on the face ab of prism abcdnear vertex b at an incident angle of 600 (see figure) if th

A ray op of monochromatic light is incident on the face ab of p-Turito

Man and mouse cells are treated with red rhodamine and Green fluorescent dyes separately and then are made to fuse. The resultant cells when kept at 37ºC, the distribution of dye on the surface of cell will be like–

Solution for the question - man and mouse cells are treated with red rhodamine and green fluorescentdyes separately and then are made to fuse. the resultant cel

Man and mouse cells are treated with red rhodamine and green fl-Turito

Which of the following statements is not correct?

Solution for the question - which of the following statements is not correct? methanol is not poisonousall alcohols are not poisonousonly lower alcohols are miscible with water