Maths-
General
Easy
Question
If
then ![tan space left parenthesis alpha plus 2 beta right parenthesis tan space left parenthesis 2 alpha plus beta right parenthesis equals](data:image/png;base64,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)
- 1
- -1
- 0
![1 half](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAjCAYAAACZ6FpfAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAJFJREFUeNpjYMAP1IC4FogvMFAIFgNxGhD/Z6ASGDVo1KBBYdB/LHgUDCbwn0w8CgYLsAbiNUD8CYh/QaujaHIMOgjEkUDMA+VrAfFRqBjFQB6IL1HLyz+oYYgl1HsUAQ4gPgmNBLKBIBBvAGI3SgxRghqiQokhGkA8G4i5KDFEHIhXATELpYG7BeoimhZyWAEAI3M1I31CbrEAAABidEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtbj4xPC9tbj48bW4+MjwvbW4+PC9tZnJhYz48L21hdGg+ND6jrQAAAABJRU5ErkJggg==)
Hint:
When we find sin cos and tan values for a triangle, we usually consider these angles: 0°, 30°, 45°, 60° and 90°. It is easy to memorise the values for these certain angles. The trigonometric values are about the knowledge of standard angles for a given triangle as per the trigonometric ratios (sine, cosine, tangent, cotangent, secant and cosecant).
The correct answer is: 1
If
then ![tan space left parenthesis alpha plus 2 beta right parenthesis tan space left parenthesis 2 alpha plus beta right parenthesis](data:image/png;base64,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)
![rightwards double arrow s in space left parenthesis alpha plus beta right parenthesis equals 1
W e space k n o w space t h a t space semicolon space sin 90 degree space equals space 1 space s o comma space space left parenthesis alpha plus beta right parenthesis space equals space 90 degree
rightwards double arrow sin space left parenthesis alpha minus beta right parenthesis equals 1 half
W e space k n o w space t h a t space semicolon space sin 30 degree space equals space 1 half space s o comma space space left parenthesis alpha minus beta right parenthesis space equals space 30 degree
F r o m space t h e space a b o v e space w e space g e t comma
space alpha space equals space 60 degree comma space beta space equals space 30 degree
N o w comma bold space bold italic t bold italic a bold italic n bold left parenthesis bold 2 bold italic alpha bold plus bold italic beta bold right parenthesis bold space bold italic t bold italic a bold italic n bold left parenthesis bold italic alpha bold plus bold 2 bold italic beta bold right parenthesis
t a n left parenthesis 2 alpha plus beta right parenthesis space t a n left parenthesis alpha plus 2 beta right parenthesis space equals space t a n left parenthesis 150 degree right parenthesis space t a n left parenthesis 120 degree right parenthesis
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space space c o t left parenthesis 60 degree right parenthesis space c o t left parenthesis 30 degree right parenthesis
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator 1 over denominator square root of 3 end fraction cross times square root of 3 space equals space 1](data:image/png;base64,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)
Related Questions to study
chemistry-
The Products (A) and (B) , respectively, are:
The Products (A) and (B) , respectively, are:
chemistry-General
maths-
The cartesian equation of the plane passing through the line of intersection of the planes
and
and perpendicular to the plane
is
The cartesian equation of the plane passing through the line of intersection of the planes
and
and perpendicular to the plane
is
maths-General
chemistry-
Identify(A) and (B) in the reaction:
![](data:image/png;base64,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)
Identify(A) and (B) in the reaction:
![](data:image/png;base64,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)
chemistry-General
maths-
If
then at
is
If
then at
is
maths-General
chemistry-
In the reaction ![3 Br subscript 2 plus 6 CO subscript 3 superscript 2 minus end superscript plus 3 straight H subscript 2 straight O not stretchy rightwards arrow 5 Br to the power of ⊖ plus BrO subscript 3 superscript ⊖ plus 6 HCO subscript 3 superscript ⊖](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAWUAAAAXCAYAAADTGF7FAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAABZ5JREFUeNrtXV9kllEYPybTRcYkk0wkmUkiSZIZk0mSMUmSGV3sIuk2XSWSLrpITBeTJCZdJNPdJMmYmWQSSdJFIpnkM+PrPN7ns3ef98/znD/vOfve58fDvu+83/ee5/f8Oec853zvlBL4QBNlTcs7LfuFEoFAIAiPLi1TWpaECoFAIIgHDaGgNtir5aGWj1pWtDzWMii6CoSveDCk5Y3QUAsc0/Jey9HUexB081pOia7iGxy+hrXMafmHs7rPWu5r2Zlxbate+l3LJy0vtOyJkARQflbLKur0EhNk1uh1D0euNdT9Vo7ugzi6/UIpG+l2q6SmvK+AxyxxDa5982DaNy5vrsDh2NavoVS1oGVXRtt29IMez3raxCTHRiF1pca2iR/7ygVGfEG2HtPSnXrvsJbXBIUu4A1jwhU01AF8DQpf1PK27bqzWha1jCJxrUQ6maH7eZXUhofx2i78ewk5aAfc+xV+X2jY2Nc2KXN5c52sTK/l+jX40J2C9inkogo9uX3n2iikrtTY5vqxz1zglK9VgkJdOKqoSAJsEMmlXPdFSy/x2s85o38vtg22zZDnPM8WbGauHPva3I/LW0xJmevXEIw/tXzNEWi7GmHfTWwUSldqbHP92GcucMrXPlwKlSnUrzafLmjiezMY9OsVB9g0cQY2jSMU9TsnC9qh7VHqNSTkgYgGKhv72tyPyxsVNxXtmKFNYuP6NcyG7pbMhsYrSsqcvpvYKJSu1Njm+rHPXOCErz4tE5jxTxcoBKMxFKhhE+tIW/sKdq47QAL6RCwZfGPU3b6WfOdu/L50X33XiU2TMtW+Lu7H5Y2KZ5hcLnhIbKZ+XVQ33KGSTZ4eT7a16buJjULpSo1trh/7zAVWfLUnkWsFCrUEpt0HM9qPBExADaw3wWbHP1zGLWLdKQ3O0nTN0TWhl+dc+9oOLr5460ObNnFWsr1AlzVM4LB6uY5B4MuvYQMKNm2Op947jEnyVEW25fbd1EYhdKXGNtePq8gFVnxBXeQcZvahAgJhxB1RyWbWIUdLag6pzYLPLeEscBuOUidwZjjl0RBVnEVuOkiaVPu6mCnb8NZkyGzJPbZhUrqJs60Bj34NZYIHWpZVch6VetLExrY2fbexUdW6UmOb68dV5QJTvjZNqxcICoGDz3tIyqYJYTVnKQKj0o/U6xUkibpk2eNhGR6ifMG1r235wgdv6ZnyNLNM1lrex+LXLssXJn2PwbddxzbXj7dULmgQCWwwyDB9JgTVcHNq40hL0SgH5xGpO8QQ+FcK2ieU2YZVyKTMsW9eW5k9ffFGrSlX5dexJWVO32PwbdexzfXjLZMLDuGyoEwhIOkvk2CTZ0JQDZd35m+gbWbYr8qL9unPwrI3qxjfo/wf7fKRlKn2pbTl2dMXb9TTF1mAeusXT34dS1Lm9D0G33Yd21w/jjIXwHJuPFWnGcZOXi5RCH4BcwNrIybO1PBguG7UZxL1AcBPHD+opN6WxhjqeSm1BO7D1+2H0cexFjSkNg6Mj6jsA+PpGeSy8vez06Zn+3Lvl2VPDm+uARtCx1P3HcWEPObZr0MmZZO+h/ZtH7HN9ePocsFJlWwONFCgHnWmpATRxGufqM2HrqkE+3wmxC5cQsBsYR3vczLnWqhHPcflMPT9t5anKtlAaEfrp5V/VLLLPUMYFQdUmHqzjX1NgqfInia8ucA4zlzW0a6wIXjUs1+HgIu+bxXfpsa2iR/XIRfkouiZEJ2GLjRuJ6NO9hTUy7drwVdMz4TwDXiQCRyBmehgHetkT0G9fLsWfFX1TIiYlpSXOnyGXBd7Curl27Xhq6pnQsQCSFa3VfERmq2MutlTUB/frg1fVT0TIjZ06n8eqas9BZ3v28JXBwN2hheFBoH4tvAlfIWfQcKoCA/I3iuUCMS3hS8KX/8B5Cjzr31Auh4AAAIfdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1uPjM8L21uPjxtc3ViPjxtaT5CcjwvbWk+PG1uPjI8L21uPjwvbXN1Yj48bW8+KzwvbW8+PG1uPjY8L21uPjxtc3Vic3VwPjxtaT5DTzwvbWk+PG1uPjM8L21uPjxtcm93Pjxtbj4yPC9tbj48bW8+JiN4MjIxMjs8L21vPjwvbXJvdz48L21zdWJzdXA+PG1vPis8L21vPjxtbj4zPC9tbj48bXN1Yj48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+SDwvbWk+PG1uPjI8L21uPjwvbXN1Yj48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+TzwvbWk+PG1vIHN0cmV0Y2h5PSJmYWxzZSI+JiN4MjE5Mjs8L21vPjxtbj41PC9tbj48bXN1cD48bWk+QnI8L21pPjxtbz4mI3gyMjk2OzwvbW8+PC9tc3VwPjxtbz4rPC9tbz48bXN1YnN1cD48bWk+QnJPPC9taT48bW4+MzwvbW4+PG1vPiYjeDIyOTY7PC9tbz48L21zdWJzdXA+PG1vPis8L21vPjxtbj42PC9tbj48bXN1YnN1cD48bWk+SENPPC9taT48bW4+MzwvbW4+PG1vPiYjeDIyOTY7PC9tbz48L21zdWJzdXA+PC9tYXRoPjejuZIAAAAASUVORK5CYII=)
In the reaction ![3 Br subscript 2 plus 6 CO subscript 3 superscript 2 minus end superscript plus 3 straight H subscript 2 straight O not stretchy rightwards arrow 5 Br to the power of ⊖ plus BrO subscript 3 superscript ⊖ plus 6 HCO subscript 3 superscript ⊖](data:image/png;base64,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)
chemistry-General
chemistry-
The product (A) formed can:
The product (A) formed can:
chemistry-General
chemistry-
Which of the following is the strongest oxidising agent?
Which of the following is the strongest oxidising agent?
chemistry-General
Maths-
Two circles with radii
, touch each other externally. If
be the angle between the direct common tangents, then
Two circles with radii
, touch each other externally. If
be the angle between the direct common tangents, then
Maths-General
Maths-
In triangle ABC, medians AD and BE are drawn. If AD=4, and
, then the area of the △ABC is
In triangle ABC, medians AD and BE are drawn. If AD=4, and
, then the area of the △ABC is
Maths-General
physics-
Two coherent sources S1 and S2 are separated by a distance four times the wavelength
of the source. The sources lie along y axis whereas a detector moves along + x-axis. Leaving the origin and far off points the number of points where maxima are observed is
Two coherent sources S1 and S2 are separated by a distance four times the wavelength
of the source. The sources lie along y axis whereas a detector moves along + x-axis. Leaving the origin and far off points the number of points where maxima are observed is
physics-General
physics-
Two coherent sources separated by distance d are radiating in phase having wavelength
. A detector moves in a big circle around the two sources in the plane of the two sources. The angular position of n = 4 interference maxima is given as
![](data:image/png;base64,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)
Two coherent sources separated by distance d are radiating in phase having wavelength
. A detector moves in a big circle around the two sources in the plane of the two sources. The angular position of n = 4 interference maxima is given as
![](data:image/png;base64,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)
physics-General
physics-
A beam with wavelength l falls on a stack of partially reflecting planes with separation d. The angle
that the beam should make with the planes so that the beams reflected from successive planes may interfere constructively is (where n =1, 2, ……)
![](data:image/png;base64,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)
A beam with wavelength l falls on a stack of partially reflecting planes with separation d. The angle
that the beam should make with the planes so that the beams reflected from successive planes may interfere constructively is (where n =1, 2, ……)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQQAAAC2CAYAAAA/ffPAAAAgAElEQVR4nO2deXAb53nGn8UNEATvAwRvEgRvkSJ1mJRIHXZle+zGjWqpjVsn7mHXjlO7TtO0k06q5ujUnbrTtGlz13WTKkflyJGasZNIpERJtCjSvMT7FA+AOImbJK7d/qHsVpQoiRJx8/vNeMYCwd2XWOyz3/d87/e+FMMwDAgEAgEAL9IBEAiE6IEIAoFA4CCCQCAQOIggEAgEDiIIBAKBgwgCgUDgIIJAIBA4iCAQCAQOIggEAoGDCAKBQOAggkAgEDiIIBAIBA4iCAQCgYMIAoFA4CCCQCAQOIggEAgEDiIIBAKBI2YFwWQyYXZ2Fk6nM9KhRD2kKBZhs8SsIHi9Xuh0OgwMDMBms0U6nKjkypUrGBgYAEVRkQ6FECPErCCkpKRAKpVieHgYU1NTsNvtkQ4p6vjiF7+Ib37zm5EOI+LQNI1AIACapiMdStQjiHQAD4tMJkNFRQWkUik6OzvhcrnQ2NgIuVwe6dCiBofDAZfLFekwIs7y8jIcDgeSk5ORnJwMHi9mn4MhJ6Y/GalUisLCQtTV1cFsNqOzs5N4CrewtrYGr9cb6TAiitlsxsjICObm5iCRSMj06T7EtCAAN0WhuroaKpUKNpsNfX19xFP4Nfn5+cjOzo50GBHDarVibGwMa2tryMjIIIKwCWJ2ynArYrEYO3fuhEQiQU9PD2QyGdRqNZKSkiIdWkR5/PHHkZmZGekwIoLNZsPExARMJhOqq6uhVqsjHVJMQMVTo5bV1VXMzc3h8uXLUKvV2LlzJxITEyMdVsTweDzg8XgQCoWRDiWsWCwWjI+PQ6vVYt++fcjOziYjg00SV4IA3BSFsbExTE1NQaFQoKmpaVuKAsMw3E1w6//HO2azGcPDw3C73dxUks/nRzqsmCHmPYTbkUqlqKysRF5eHpxOJz766KNt6SlQFIW2tjZ0d3dvGzGwWq0YHR2F1+tFUVER8vPziRg8IHEnCMBNT6G+vh4lJSWYmprC5OTkthSFt956Cz/4wQ8iHUZYsFqtGB8fx/LyMgoLC1FRURHpkGKSuDAVN0IsFnN5Ch0dHVhdXUV9ff22mj4YjUakpqZGOoyQw3oGi4uL2L9/P5RKZaRDilnicoTAIpFIUFhYiD179kCv1+PKlSvbKk/B4/HA5/NFOoyQYjKZMDQ0BKvViqamJmRkZEQ6pJgmrgUBuCkK5eXlKCgogNvtRnd397aZPqhUqri+QZaXlzE6Ogqfz4eSkhLk5uZCIIjbQW9Y2BafnlgsRl1dHYRCIfr7+yGXy6FWq5GSkhLp0ELKkSNHkJWVFekwQgLrGdjtdmg0GpSVlYX8nAzDwOPxQCAQxK3wxN2y471YW1vDjRs3cPHiRVRWVmLHjh1QKBSRDitk0DQNiqLibpXh9jyDcHkGLpcL4+PjyM3NRWZmZtx9rkAUjRBMJhNMJhOysrKQkpISkg0orKfg8/m4term5ua4NBoZhuE+w3jKQzCZTBgZGYHT6URzc3PYMjFZETIYDEhPT4+bz/N2osZDoCgKdrsdXV1d0Ov1ITuPRCJBWVkZiouLsbKygq6urrj0FCiKQnt7O3p6euLmy2uxWDAyMgKfz4eysjLk5OSEJc/AbDZjcnISJpMJBQUFSE5ODvk5I0XUCIJCoUBqaiqMRiPGx8extLQUsnOxnkJhYSEWFxcxPj4Oq9UasvNFiv/4j//AmTNnIh1GUGA9A6fTifz8/LB5Bna7HZOTkzAajcjIyEBtbW1c75GJmimDSCRCSUkJpFIp2tvbsbKygj179iA9PT1k56uqqoJMJsPFixfh8/lQW1sbV57C6OhoXJRPs1gsmJiYgFarRXNzM3JycsJyXrfbjevXr8NoNCI3NxeNjY1xX0shqv46gUCAnJwcNDc3w+fzob29HWazOWTnE4vFKCwsxL59+7CwsBB39RR8Ph8CgUCkw9gSRqMRQ0NDMJvN2L9/f9hWTZaXlzEwMACDwYCysjLU1NTEvRgAUSYIwE1RKCoqgkajgUgkwtWrV0M6fZBIJCgtLUVpaSlWVlbw4YcfbugpBAKBmLu5MjMzY3pplS1u4vP5UF5ejuzs7LB4BiaTids6XVJSgsLCQkil0pCfNxrgnzhx4kSkg7gdHo+H1NRUCIVCTExMwOv1QiwWh2w1QCAQICMjA16vFzMzM6BpGnK5fN2XQK/Xw+fzQSaThSSGUGCxWFBZWYmamppIh/LAsMVNXC4XioqKwuoZTExMwGw2IzMzE3V1ddtGDIAo8hBuh8/no7CwEGKxGOfPn8fa2hqEQmHIMu9u9xT8fj+qq6u5J+zY2BgUCkXIPI1Q8Gd/9meRDuGhMJvNmJiYgE6nQ1NTE1QqVVjO63K5MDQ0BJPJBJVKtS08g9uJ6r9WIBBAqVSipaUFHo8nbJ5Ca2srfvnLX+JrX/saBgcHAdycjy8vL8dk0dJYMhYtFgs6Oztx/fp1tLS0hC3piPUM9Ho91Go1amtrt50YAFE8QmARCAQoKCiA1+vFxMQErly5gt27d4esCs6tnsKpU6fQ09ODN998EwzDYGFhAV6vF08++WRMfFnOnz+PxMRE7N69O9Kh3JNAIICFhQX09fWhra0Ns7OzqKysRHp6elg+Z5PJhKmpKZjNZpSVlaGoqAgSiSTk541Gol4QgJvTB7VaDYFAgKtXr2J0dBQ0TYdsKCkQCHDkyBFMTU3hv//7v/Gtb30LRUVFmJ6ehs/nwxNPPBGS8wabkydPoqCgIKoEgaZpeDweOJ1OLC8vY35+HouLi5iamsKlS5fQ2dmJlJQUlJeXh3xkwzAMbDYbJwbZ2dkoLy+HSCQK6XmjmZgQBOCmKBQVFXGegsfjgVAoDEnqaiAQQHZ2Nl555RWkp6fjs5/9LHbv3g2HwwEejwe/3x8TlXj6+vqwtrYW6TDW4fP5YDQaMTIygsuXL+Ps2bMYGRlZt4KTn5+P6urqkGZYMgwDl8uF4eFhmEwm5OTkYPfu3XGT1fmwxIwgADdFQalUorW1FX19fbhw4QIOHTqEtLS0oF1Ij8eDvr4+GAwG+Hw+SKVS/OZv/ia3/FlaWgqLxRK25JitwDBM1PkHIpGI25bd1NSE3//938eZM2fwve99DxMTEwCAkpISHDlyJKTTBavVipGREej1epSXl0OtVm97MQCi3FTcCIFAgPz8fFRWVkIqleLSpUvQ6/VB++KznoVcLofVasXU1BSmp6e5XAij0YhTp07BYrEE5XyhRKFQRF0nK4qiIBAIIJPJuFZ8vb29EIlE+O3f/m1UVVWhqqoKSqUyZDeo0WjE2NgYTCYTNBoNN/IkxNgIgeVWT+HatWsYHh5GIBCASqXa8peIHYVQFAWhUMjNMzMyMqDVauF2u3Hy5Ek0NTUhLS0tSH9RaPit3/qtqK2HYDKZ0NbWhu9+97twOp14/PHHOSOxuLg4JOdkGIYTeXaUxybAEW4Sk4IA3Okp+P1+zlMIxpMlOzsb2dnZaGlpwYsvvoj5+Xl0dXWhra0N586dw8zMDKqqqqI6aeX1118HEH3bn+12OwYHB/Huu+/CaDTiueeew2uvvYZTp04hJycnJCLGegYjIyMwm81QKpXEM9iAmC+QEggEsLi4iJ6eHgQCARw8eDAk+9VpmobP54PL5cKNGzcwODiInJwcPPLII1G/ISqaBIHdzarX66FSqZCUlMSVPvvxj3+MoqIiVFdXBz0BzWq1YmhoCAaDARqNBuXl5duugc1miHlBAG6KwvT0NCYmJuDxeNDU1BTSbj0Mw2BwcBAzMzMQiURobm6Oyj3y0ZaHwG5UomkapaWlyMrK4kZYXq8X4+PjUCqVQTWJ2fNOTU1xG5UKCwuRkJAQtOPHEzFnKm4En89HSUkJNBoNfD4fhoaGoNVq7zAaGYYJygYliqJQWVmJgoICOJ1ODAwMRKXJ+OMf/xi/+tWvIh0GGIaB2WzG6Ogo/H4/8vPz79gwJBQKUV5eHvTRncVi4TyD3NxclJaWEjG4BzHrIdwOn89HcXExJBIJzp07B5qmIRAI1nU/9ng8cDgcQcmAEwqFqK6u5lY6hEIhKioqomp3YVdXV1Rs52brGVgsFuzatQt5eXl3vIc1cYMFwzBwOp0YGRmBxWKBUqlEY2Nj1EydopW4GCGw8Pl85OTk4PDhw3A4HLh06RKWl5e5n5vNZvT29sLv9wflfCKRCMXFxTh48CAmJydx7do12O32oBw7GAgEgognUBmNRgwPD0Ov16OlpQW5ublhOa/NZkN/fz8MBgNKSkrQ0NBAxGATxJUgADdFQaVSoaGhAX6/H//0T/+Ey5cvg6Zp8Hg8mM1m2Gy2oOUtiMViFBQUoK6uDisrK7h06VLU1Gj0+/1BE7+HwWAw4Pr16/B4PNi1a1fQvYF7nZddTaisrERJSUnclk0PNlFZD2Gr8Hg8pKSkwOVyob29HRcvXkRSUhLkcjnm5+dhsViQnJwctKQdPp+PtLQ0eDweGAwGOBwOJCYmRrx2gtPpRH19PXbs2BHW8zIMwxVEDQQCKCoqQlFRUcjFwGw2w+FwYHZ2FhaLBXl5eSgvL4/qpeFoI65ls7q6Gk899RReeeUV8Hg8PPHEE3C73Th37hzS09PX+QtbhfUUJBIJrly5ArFYDIqiIpq89Bd/8RcAwr/syHoGNpsNO3fuRH5+fkjO4/P54PF4YLfbsbi4iNnZWa6ITmZmJnbu3EmmCQ9IXCw73guv14tf/OIX+NKXvgStVosDBw7g/fffx3e/+10cPXo06OfzeDxYWFjApUuXoFKpsGfPnriu0ns7t6YFHzhwAKmpqSG5KW02GyYmJvDhhx/i7NmzGB0dhUajwbPPPovDhw+jpKQk4v5JLBK3I4SFhQXMz89jZWUFALBz5044nU588MEHsNlsITP/xGIx8vPz0djYiMnJSXR0dGD//v0RyVNoa2tDYmIidu3aFZbzGQwGDA0NIRAIYO/evUhJSQmKGPj9ftjtdszPz+P69eu4dOkSBgYGsLa2BqfTCZ1OB4ZhUFFRgR07dhAx2AJxZyqysAUutFotZmdn4Xa74XQ6uf4L3d3dGBsbC8m5RSIRysvLUVhYCI/Hg48++iiklZ7uxk9+8pOw5CEwDMN1VAKA4uJiqFSqoO1WZDdESaVSJCcnc70cbTYbbty4Aa/Xi7S0NDz99NOoqKggYrAF4naEkJGRAZlMBoqiMDw8DABITU0FTdNwuVzo6OjgUlhDgVAoRE1NDSQSCTo7OyGVSsPuKXR2doZlxYP1DBwOB+rq6lBQUBDU4/P5fCQlJSEpKYm7XhMTEzhx4gQuXLiApaUlFBUV4Xd/93ejKg8kFolbQQCAhIQE7N27F3v27MEf/dEfwWAwoKurC5cvX8bp06e5vIFQzfGFQiFKS0shFotx8eJFuN1u7Nq1K2zTB5FIFPJ8fYPBgPHxcc4zCIfg/epXv8I///M/Y3x8HE1NTfB6vSgpKQlbn8d4Ju5NxdtxuVyw2WwYHx/H4uIipFIpWlpakJWVFTJH2uv1YnJyEmNjYxAKhWhpaQmLKKjValRXV+P06dMhOb5er8fw8DD8fj9qa2uRlZUV8hqI7733Ht5++23Mzs7imWeeQVpaGpaWlpCeno4///M/D+m5twNxmYdwL0QiERQKBYqLi5GSkgKj0Qij0QiJRAKFQhESUeDz+UhJSYHP54PFYoHZbEZSUlJY8hT27NmD6urqoB6T9QzYqVhxcTHy8/PDssTX2dkJnU6HiooKPP/881hbW4NcLkd1dTUKCwtDfv54Z9uNEG6FpmlotVq0tbVBqVSisrIyKEVW7obP58PExAS6urqg0Wig0WhC1ufh1tyDYOchmEwmrkFubW1t0D2DjaBpGg6HA11dXXA4HCguLkZDQwPOnTuHhIQE1NbWkk1LQWBbCwJwc+u0Xq9HR0cHRCIR9u/fj4yMjJBOHxYWFnDhwgUUFBSgsbExKrdO3w3WMzAajTh48GDYTFKbzYaBgQGYzWaUlpaitrYWFEXB4XBAKBSSbMQgse0FAbj59Jmbm8PIyAgcDgcOHjwYck9henoaw8PDEIlEIfMUPvroI8hkMlRUVATleHq9HkNDQ/D7/aivr0dGRkZY+iawRVWMRiOqq6tRUFDALStHU/GXeCBu8xAeBB6Ph4KCAmg0GshkMnR3d2NhYSFkFYtFIhHXDMbv9+Pq1ashyVP4r//6L/z85z/f8nEYhuF2LfJ4PJSVlYXFQARujkgmJiZgtVqhVqvXiQEAIgZBhgjCr+HxeCguLkZ9fT1sNhvGxsawuLgYMlEQCoWoqqqCRqOBXq/n0n2Dyblz59DV1bWlY7DFTcbHx7G2tobi4uKQFUG9FZqmYbVaOTHIzs7m8joIoYMIwi3weDzk5ubi8OHDMJvN6O7uhtFoDKkoqNVqtLS0YGxsDIODg1wmZTCQSqVbvoHYvQkGgwF79+4Nm5PvcDgwMDAAk8mE/Px87Nq1i4wGwgARhNvg8XjIzs5GU1MTV9HZYDCEdPqQm5uL/fv3Y3l5GR0dHUHLLnQ6nXC73Q/9+0tLS7h+/TqcTidaW1vDlgVoNBoxODgIi8WCqqoqlJeXEzEIE9suD2EzUBQFhUIBPp8Ph8OBxcVFyGSykOcp+P1+2Gw26HQ6pKSkbDlPQSwWY+/evQ9sKrKewdDQEPh8PsrKyu65HBtMY0+v13Nbp9VqNVcWjxAeyCrDPaBpGouLi+jo6EBmZibKy8uRl5cXlC9/f38/TCYTaJqGRCLB/v37wePxMDQ0hN7eXhQVFUGj0YQ9HZdNOhobG4Pb7UZFRcW6acLCwgImJycRCARA0zR27NgRlLoSrGcwMjICm82G7OxsNDQ0xESX7XiCCMJ9oGkaer0e7e3tkMlkeOSRR7a8JOlyuXD06FG0tbXB7/dDKpVicHAQpaWl8Pl8mJ+fR1tbG0pKSlBXV4fU1NSHOg97aR8kVtbVNxqNaG1tvSNx6ktf+hLefPNNblv517/+dXz6059+qPhuha2BuLy8jOLiYtTV1W35mIQHh0wZ7gNFUUhISEBKSgpXSjwzMxMJCQkPdKOxw+re3l7s2bMHr732Gv7hH/4BTz31FORyOQwGA9LS0pCZmQm5XI7k5GTMzMxAq9Wu61/wIAwNDcHpdG5aUJaWljA0NISVlRXs27fvjuImjY2NkMvl+Pa3v42XX34ZKSkpcLvdoGl6SysP7PTEYrGgpqYGarWabGGOEEQQNgFFUUhMTIRAIIDL5cLc3BxkMhmSkpI2LQoUReHcuXM4efIkGhoa8Hu/93soLCxEVlYWrFYr9Ho9CgsLkZOTAz6fz3WDslqt0Gq1SE1NfWBP4ctf/jK0Wi327dt3z/cxDMMVNxEIBNBoNOuarep0Ovzd3/0dUlJScOzYMezduxdZWVlYW1uD0WiEWCxGTU3NA8XGsrS0hMnJSVitVmg0mjvyDAjhJa63PwcTHo+HoqIiCIVCXL58mSuustlNPX6/Hx988AF0Ot263Yc+nw88Hg9CoXDdfFkoFKKyshI8Hg/9/f0YHh5GeXn5A/U9bGtrQ2Vl5T3fw3oG4+PjCAQCXPLPrfT39+Ps2bN47733UFpayr3OFi55mKc5TdNYXl7G5OQkHA4HVCoVysvLiWcQYYggPABsnsLBgwfR1taGvr4+iESi+2btMQyDDz74AIFAALt27cLa2hpomoZQKIROp8PMzAz4fP4dpcLZp7VMJsP58+e55jOb3T+wmTwEo9GIiYkJmM1mtLS03NFTsa+vD/39/Zzp6ff74fP5sLa2hsnJSTidzgfunswwDBwOB4aGhmC1WlFYWIj6+voHOgYhNBBT8SFgd0n29/fD4XDg8OHD9zUaP/GJT+C9997D6uoqUlJSwDAM+Hw+vF4vJBIJ3nzzTTz99NMb7n70er2Yn59HT08PV79hMzkBlZWVqKysxKlTpzb8uU6nw8jICNbW1tDc3IykpKQ7hO0b3/gGTpw4AaPRyE2bgJvi6HA48PLLL+PVV1+FWq2+bzwsRqMRo6OjMJvNqKmp4UZehMhDRggPAY/Hg0qlgs/nw9jYGC5fvozdu3dvuCRJ0zRmZ2cxNjaGJ554Ak899RTsdjt4PB5cLheuXLmCy5cvo6am5q5boUUiEQoKCrC6uoq5uTl0d3ejubmZ2+57tzyAz33uc3c9psViwY0bN5CYmIjq6uoNBcbpdOL69etITU3Fl7/8ZXi9XtA0Da/Xi7m5OXznO9+BUql8IDFgPQObzYaqqirk5eURMYgiiCA8JDweD4WFhRAIBOjs7MTo6ChomkZBQcG6m9PpdKKvrw8JCQk4duwYjh8/zv3MYDBAKBRyDVDvBVuj0e/34+c//zlmZ2dRUVGBioqKu7ZO/+QnP7nh61qtFhcvXsTs7Cyqq6vX+QysuLAdrh0OB/bt24cXX3xx3THOnDmDsbExaDSa+35WwE1htFgsnGeQm5tLVhOiECIIW4D1FFpbW3H+/Hl4PB6IRCJkZ2dzQ2+Xy4WxsTFUVlbe8bR+//33MTw8jGeffXbTy4perxezs7N45513UFNTgxdeeAFPP/30Xd9/+8jBYrFgaGgIHR0d0Ol0WFpagt/vx2OPPXZHJubo6CgSExPvKEQ7MDCAU6dO4dChQ5vKgmQYBna7HcPDw7DZbCgoKCCeQZRCLN0twuPxkJWVhQMHDgAA2tvbYTQaQdM0gJuNW3Q6HdLT09cVc9XpdDh37hwsFgs+9alPcR2H7sU//uM/4o033oDD4cCnP/1p7Nu3D36//64boqampjA/P7/unP39/fB6vfjbv/1bvPLKK0hNTcX3v/99PPPMM5ibm+PeyzAMlpaWwOfz12UiulwudHV1obOzEx/72Mc2VbXaZDJhYGAAFosFFRUVD71ESQg9RBCCAI/HQ05ODmpqapCamoqOjg4sLi4CuDn/l0qlmJ2dhcfjAQDY7Xa88MILCAQCeP311+/biNTn8+GnP/0pPvroI+zYsQOf//zncfz4cfzGb/wGV9F5o3oKb731Fn70ox8B+P+kI4qi0NDQgKysLDQ1NeFTn/oUjh07Bp/Ph3feeWddr4qEhARYLBbodDrutTfffBNvv/02vvCFL2wqGUmn02FsbAw2m40rbkIar0Yv5MoECbbICo/HQ1dXF0ZGRsDj8aBQKHDw4EH89V//Nf793/8ds7OzMJlMEAgEeOaZZ3D48OH7HttqteLf/u3foFar8cILL6CxsREAuH0OQ0NDGBwcRGVl5bqn+YULF6DX6+H1ejE2NsbVfMjJyQEAKBQKKBQKKJVK2Gw2vP3229wUgaIotLa24tq1a/jBD36ApKQk+Hw+3LhxA83NzXj++efvOf9n8xumpqbgcDhQUFCA0tJS4hlEOwwhqAQCAWZpaYn5/ve/z/zsZz9jTCYTwzAM09raygBgEhMTmV27dnGv3w+appne3l4mOTmZ+fa3v33Hz30+HzM1NcV85zvfYdrb2xmj0cj9bN++fcyTTz7JDA4OMqdPn2YMBsNdz7O2tsaUlJQwn/zkJxmHw8G9/pWvfIUBwMjlckalUjGnT5/e1GewvLzMtLe3M6dPn2Z6e3s39bcSIg8ZIQQZHo+HzMxMHDp0CN3d3fjFL36Bw4cP47333gPDMKBpmutEtBlsNhvm5uZQW1sLlUp1x88FAgHy8/Nx+PBhdHZ2wuFwoLW1FUlJSaipqYHVaoXBYMDBgwe5dOiNEIvFaGxsREpKCvR6PedpvPHGG3jppZdAURQoioJcLr9vzKxxuby8jJqaGpSUlGzqbyVEHuIhhAC2yEptbS3S0tJw4cIFeL1epKSkIC0tDcnJyZveA2G32zE9PY3i4uK7blISCoXIy8tDfX09t2diaGgIZWVlOHLkCGpraze176KkpAR+vx+Tk5Pca1KpFOnp6UhLS0NqaipEItE9i8WwyU52ux21tbXIz88n04QYgowQQgS79yEpKQnd3d0YGRnB6urqA/cw4PP5WF1dhUqlumcPB4FAgMrKSiQkJGB0dBQrKytobW1FQUHBpnc77t27l0ujvhd3Exaz2cyZqWRkEJtsKAhutxt2ux1ra2vhjieu4PP58Pv9SExMxKVLl2AymcAwDIRCIXw+H7c0eTckEgnXNzEQCGB6ehoymeyu14XP52NlZQUJCQnQ6/UoKiriruW9nuo8Ho+byshkMlitVszOzoKiqPvGSFEUhEIhaJrGyMgIFhYWkJqaivz8fMzOzgJAyMrPbQcoikJycvK6tPGQno/Z4GqdPn0a//Iv/4KOjg7weDxSz24LsB+vUqnExz/+cSiVSvzwhz/E1NQU1tbW7ru7j6ZpBAIBADdv+Pu9n2EY7j+JRAKGYeDz+TZ1DWmaBk3ToChqU8N85tdZjSUlJWhtbYVCocD58+fR19cHPp9PvjdbxOfzQSaT4Qtf+AKee+65sHTI2lAQhoeH0dvbyyW8kAv78DAMAx6PB7lcjtTUVNjtdnR3dyMjIwMKhQICgeCuT2H2d9mbky1bdr/rwefzwefz8Td/8zfIzs7Gq6++itXV1fvGyhqHAO47MgBujiyWl5exurqKtLQ0lJaWwuVywWq1klFBEAgEAhAKhThw4ABKSkrCUidiQ0Gw2Wxwu90Qi8UhD2C7wDAM3G43TCYT9Ho9BAIB8vLyuK3TwbyB2K3U+/fvh1qtxsmTJ2G324N2fHavw/LyMnQ6HVZWVpCUlASlUomEhARiIgYJ9oEQrnZ5wF08BHZY6vP5whbIdkAqlUKlUkEqlaKvrw+rq6vw+/3IzMzkPvNgCANN02AYBoFAAIFAAD6fL2jXkqIoBAIBuFwuTE1NYXV1FZmZmZyByE47CFuHFQS/3x+27M4NzyIQCCCRSEj1mhChVCohFovR39+P69evY8+ePUhLSwOfzw+KILAjBIqiwOPxIJFIuLTprUJRFJaXlzEzMwOXywW1Wo2ioqKgHJuwHtajCed9eHjdiYoAAA1cSURBVFdBEIvFxDsIERRFQalUAri5Aenq1at45JFHoFQqIRAIOBPxYeHxeODxePjjP/5jpKeng2GYB65qtBF8Ph9arRYzMzNwu92ora1FdnY2JBIJGRXECRt6CH6/H4FAgAhCCGGHglqtFtevXwdFUdBoNFyNhWDcYAaDAQKBgBOFh4X1DJaWljA1NQW3283tTRCLxUQMQgQ7QhAKhWG7FzcUBHYOSggtbJ6CwWDAhQsXkJSUhMrKSuTl5XHG3Fauw62rEw8LRVHw+/2w2+0YHByE2+1Gbm4u1zeBfE9CTzhNWlJTMQpgft067cqVK/B4PGhtbV1XZOVh0ev1EAqFW3apTSYTBgcHubJnm6mBQIhNiGsYBVAUhczMTOzatQtpaWk4f/48tFrtlofir7/+Ot56660tHUOr1WJoaAh2ux319fVhaQVPiBxkL0OUQFEUcnNzQdM0PB4Pent74fF4UFxc/NAjhYGBAfj9/oeOSafTYXJyEm63m+trSQqixjdkhBBFUBSF/Px87Nq1CysrKxgfH8fc3NxDjxQkEslDrS4EAgGYzWaMj4/D5XIhNzcXlZWVRAy2AUQQogyKopCVlYVDhw5hdXUVXV1d0Ov1D2UMPmxXJavVisHBQVitVq7hLGF7QAQhCmE9hb179yI1NRXnzp2DTqd74JHCH/7hH+JjH/vYA/2OVqvlDMT6+nqyhXmbQTyEKIWiKKhUKi71uKen54E9haeeeuqBpgxarRYTExNYWVlBRUUFVCpVUBKaCLEDWXaMcphfd2a+cOECFAoFl7z0IFMBNsHlbgQCAa7s2crKyro8A8L2gghCDMD8uoLxxYsXQdM09u3bh+zs7PuKAlsH4V4bYxiGgcViwcDAAOx2O9cNirA9IR5CDEBRFDIyMtDU1ISUlJRNewrHjx/HX/7lX97zPTqdDoODg1yewa3t3gnbD+IhxAgURSEnJ4fb0nzt2jXU1taipKTkrp7C6OjoPf2GxcVFLs+gqqoKKpWKLC1uc8gIIYagKAp5eXmoq6uD3+/HxMQEZmZm7rokKRaLN7zBA4EADAYDZyDm5+dDo9EQA5FABCHWoCgK2dnZOHjwIFZWVtDb24ulpaUNRUEqld5RdoutdMSmIxcVFWHHjh3hCp8Q5RBBiEFYT2Hfvn1ISkriPIXbReG5557D448/vu411jOw2Wyoq6tDWVlZOEMnRDlklSGGYRgGi4uLGBkZgcPhQF1d3TpPYWFhASKRCFlZWdy/b92bUFBQQKYJhHUQQYhxGIaBXq/H5cuXIZPJUFZWhuLi4nVLkn6/H2azmWsWk5eXh9ra2ghGTYhWiCDEAQzDwGw2o729HTweD3v27EFOTg5WV1fBMAw8Hg8GBgbgdDqhVqtRVVUV6ZAJUQoRhDiBzWjs7++H0WjEkSNH8Oqrr0Iul+Pll1/G4uIidu7cua4aE4FwO3fkIdwvzZUQnbCrDy0tLZicnMTMzAz8fj/4fD6EQiEOHTqE5OTkSIcZd4SzRHo47s0NRwg3btzA0NAQdDodEYcYgq3RaDabMTo6isnJSSgUCtTV1UGtVnMNYcigcOuwoyybzcb1XdxKMZqNoGkaAoEA9fX1UKvVSExMDOrxN2JDaevr68O//uu/4vLly6S3YwzCtn9j9zH09vZiZWWFCEGQYAvP3tr8hh2JPSi3Nui5/frc2tsxPT09LIKw4QhhcXHxofbfE6IDti/DT37yE6SkpOCJJ56Ax+MhghAkJBIJxsbG8O677+LUqVNobW3F7/zO72D37t3wer2bPg7bRAfAht21GIYBn89HeXk5FApFUP+Gu7HhCEEulyMnJ4fktccwFEXh2WefhVAohEqlIuIeRORyOQYGBtDV1QXgZu3KRx99FLW1tbBYLJua68tkMgwMDOCzn/0svF4vXnzxRRw/fhxut5t7D3uccIkBcJdMRbYVGCF2YRgGNTU1UKvVW+4ERbgJRVHg8/mYnp5GT08PFhYWANz0EQYGBnD9+nXuqb6ZY/F4PNA0jWvXruHGjRt3JImx3bjDef3u2cqN9HaMbRYWFiAQCJCWlkamC0GAFYSOjg7cuHED1dXVGBoaQm1tLQKBAE6fPo3XXnsNEomEq0XBcmufRvY4paWlOHHiBL75zW8iPz8ffD5/3d4T9nfC6eGR3o5xCI/Hg0AgwB/8wR+gsLAQb731FlZXVyMdVlzg9/vR2dmJ3NxcvP766zhy5Ag+//nPw+v14t1334VIJIJEIrnjRmY7ObNt2Xg8HpaXl9HT0wOZTIb09HTw+fx1o4SoEQT2C0UEITbh8/ng8XiYm5uDVCoFADIF3CJ8Ph9utxttbW04cuQIGhoauKe5XC7HgQMHkJGRgatXr6Kurg7p6encMiRN0xCLxTCZTHj11VcxNTUFmUyG/Px8qFQqlJeXQ6VSAVh/nSKRE3RXQSBiELuwUz2v18s51yQ7cWuwD0m5XI76+nrk5+djdnaWm+MrFAocPnwYw8PD3CiA/cyFQiEmJibwP//zP1hcXERxcTHkcjmWl5fR0dGBV155BQUFBQA2vk4RHyGEe5hCCA3JycmcQ038oK0jkUjQ3NwMsVgM4M5GtxKJBA0NDdy/b/3MT548ie9973v46le/iueffx4A8K1vfQt/8id/gi9+8YvcjtRIXycyjoxjWltbkZOTE+kw4gaKou4oOLMZurq6MDo6CrVajU984hMAAIvFAgAoLi5GXl5eUOPcCkQQ4piXXnqJ5JJEAf39/ZDL5WhsbOQ8ArfbDYqi0NjYGJYMxM1CBCFOYRgGubm53P+TKWDkmJ2dhVAoXLftfHh4GB9++CEaGxuRkJAQwejWQyaWcQpFUZifn4derydiEGGsVisCgQC329TpdOL9999HT08PqqqqIJPJIhzh/0MEIY75q7/6K3z961+PdBjbHnaawKaPnzhxAmfOnEFGRgaSk5OjagWICEIcMz09jcXFxUiHse05cuQItFotHnvsMRQXF6O4uBg7duxAe3s73njjjai6RsRDiGNWVlZIhmIUsHfvXqytraG0tBQCgQCPPvooNBoNKioqkJaWhqSkpEiHyEEEIY65NQ+BsHUCgQD0ej0yMzPXrd6wHk0gEIDdbkdiYuK6n2dmZuLYsWM4duwY95pGo8Gjjz7K/TtajF8yZYhj9u7di5qamkiHETesrKzg3XffxfT09LrX2RtZp9Ph4sWLsFqtD3zsaBADgBRZjWsMBgOEQiFSU1MjHUpcQNM0dDod/v7v/x4NDQ04duwYUlJS8LOf/Qy5ubn40Y9+hCNHjmDnzp2Qy+WRDvehIFOGOIVhGC4dNlqGo7EOj8fjcjv+93//F1qtFoFAAL/85S+hUCig1+uhVqtjVgwAMmWIWyiKwszMDLRaLRGDIPPkk0+CYRh89atfBU3T+OlPf4re3l7U19dDqVRGOrwtQQQhjvna176GH/7wh5EOI+548skncfjwYaytrQEA5ufnkZGRgaNHj8Z8IRoiCHFMT08PRkZGIh1GXKLRaNDY2AgAKC8vR1NTE5RKZcyPxoggxDEOh2Nd0U5C8Ni5cydeeuklAEBLSwuam5sjHFFwIKZiHKNUKpGZmRnpMOKS1NRUHD16FGfPnsXHP/5xVFRURDqkoLChIPh8Pni9Xvj9/pgfAm1H2EYteXl5SE1NRSAQICOFIMN2yfrMZz6DsrIyrK6u3tFXYauwq0NisRhCoTAsxVM2zEM4e/YsvvGNb5DOTTEMRVGwWq3g8/lQKBQxb3ZFKz6fDwKBgGuTF+xjy2QyfO5zn8Px48eRn58f1ONvxIYjBJVKhccffxw7duwAED1ZVITNwzAMkpOTEQgE4HQ6yTUMEXw+HzRNh0RwA4EARCIR9u/fH7bksg1HCFarFW63+6HKRRGiA4qiMD09DbFYjLy8PNK5KQZhS7enpaVx/w61sN+16jKAB+pTR4geWA/hP//zP6FUKvGZz3yGWzMnxA6sILAt58MxyrtroxapVEqGmTEK24qvu7ubayNORgixR9Q0amE7NxFiE4FAAIFAgNXVVXi9XvD5fIjFYmIsxiBRIQjRVNKJ8OCwI4TExESugCfp3BS7RFwQWA+BTBliE/b6NTQ0cDX/iSDELuG8D0k9hDhmZWUFPB6PrBYRNg0RBAKBwEE2NxEIBA4iCAQCgYMIAoFA4CCCQCAQOIggEAgEDiIIBAKBgwgCgUDgIIJAIBA4iCAQCAQOIggEAoGDCAKBQOAggkAgEDiIIBAIBA4iCAQCgWPDqhkMw4SstDSBQHgw2N4oESuyevXqVbzzzjs4c+YMeDxeWDrGEAiE9fh8PkilUvzpn/4pjh49ylW/CiUbCoJIJEJhYSEee+yxsBd5JBAINwkEAhCLxaipqUFSUlJYzrlhxSSdTgeLxQKZTBaWIAgEwp3QNA0+n4/i4mIAEWzUIhQKIRKJiIdAIEQYhmHg8/kgFAoj5yGIRCLI5XLiHRAIEYTt3BTxMuwikQgymYx4BwRCBGGnCOF8MN+zcxMRBAIhckSilRspw04gEDiISUAgEDiIIBAIBA4iCAQCgYMIAoFA4Pg/mq/R9XYwCZsAAAAASUVORK5CYII=)
physics-General
physics-
Two ideal slits
and
are at a distance d apart and illuminated by light of wavelength
passing through an ideal source slit S placed on the line through
as shown. The distance between the planes of slits and the source slit is D. A screen is held at a distance D from the plane of the slits. The minimum value of d for which there is darkness at O is
![](data:image/png;base64,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)
Two ideal slits
and
are at a distance d apart and illuminated by light of wavelength
passing through an ideal source slit S placed on the line through
as shown. The distance between the planes of slits and the source slit is D. A screen is held at a distance D from the plane of the slits. The minimum value of d for which there is darkness at O is
![](data:image/png;base64,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)
physics-General
physics-
A monochromatic beam of light falls on YDSE apparatus at some angle (say
) as shown in figure. A thin sheet of glass is inserted in front of the lower slit
. The central bright fringe (path difference = 0) will be obtained
![](data:image/png;base64,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)
A monochromatic beam of light falls on YDSE apparatus at some angle (say
) as shown in figure. A thin sheet of glass is inserted in front of the lower slit
. The central bright fringe (path difference = 0) will be obtained
![](data:image/png;base64,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)
physics-General
maths-
Find the sum of the infinite series ![fraction numerator 1 over denominator 1.3 end fraction plus fraction numerator 1 over denominator 2.5 end fraction plus fraction numerator 1 over denominator 3.7 end fraction plus fraction numerator 1 over denominator 4.9 end fraction plus horizontal ellipsis horizontal ellipsis straight infinity](data:image/png;base64,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)
Find the sum of the infinite series ![fraction numerator 1 over denominator 1.3 end fraction plus fraction numerator 1 over denominator 2.5 end fraction plus fraction numerator 1 over denominator 3.7 end fraction plus fraction numerator 1 over denominator 4.9 end fraction plus horizontal ellipsis horizontal ellipsis straight infinity](data:image/png;base64,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)
maths-General