Question
The figure shows four pairs of polarizing sheets, seen face-on. Each pair is mounted in the path of initially unpolarized light. The polarizing direction of each sheet (indicated by the dashed line) is referenced to either a horizontal x-axis or a vertical y axis. Rank the pair according to the fraction of the initial intensity that they pass, greatest first
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)
- (i) > (ii) > (iii) > (iv)
- (i) > (iv) > (ii) > (iii)
- (i) > (iii) > (ii) > (iv)
- (iv) > (iii) > (ii) > (i)
The correct answer is: (i) > (iv) > (ii) > (iii)
Related Questions to study
The figure here gives the electric field of an EM wave at a certain point and a certain instant. The wave is transporting energy in the negative z direction. What is the direction of the magnetic field of the wave at that point and instant
![](data:image/png;base64,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)
The figure here gives the electric field of an EM wave at a certain point and a certain instant. The wave is transporting energy in the negative z direction. What is the direction of the magnetic field of the wave at that point and instant
![](data:image/png;base64,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)
In the set up shown in Fig the two slits,
and
are not equidistant from the slit S. The central fringe at O is then
![](data:image/png;base64,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)
In the set up shown in Fig the two slits,
and
are not equidistant from the slit S. The central fringe at O is then
![](data:image/png;base64,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)
In a Young’s double slit experimental arrangement shown here, if a mica sheet of thickness t and refractive index
is placed in front of the slit
then the path difference ![left parenthesis S subscript 1 end subscript P minus S subscript 2 end subscript P right parenthesis](data:image/png;base64,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)
![](data:image/png;base64,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)
In a Young’s double slit experimental arrangement shown here, if a mica sheet of thickness t and refractive index
is placed in front of the slit
then the path difference ![left parenthesis S subscript 1 end subscript P minus S subscript 2 end subscript P right parenthesis](data:image/png;base64,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)
![](data:image/png;base64,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)
The compound (A) is :
The compound (A) is :
A) Requires 2 mol of for its saturation
B) Reduces ammoniacal and gives yellow colour with
C) does not reduce Tollens reagent but gives iodoform test
D) n dehydration with conc. gives a mixture of colourless gases
The compound (A) is:
A) Requires 2 mol of for its saturation
B) Reduces ammoniacal and gives yellow colour with
C) does not reduce Tollens reagent but gives iodoform test
D) n dehydration with conc. gives a mixture of colourless gases
The compound (A) is:
Gives positive Tollens test but negative iodoform test (C) Gives negative Tollens test but positive iodoform test The compound (A) is:
Gives positive Tollens test but negative iodoform test (C) Gives negative Tollens test but positive iodoform test The compound (A) is:
Redox equations are balanced either by ion-electron method or by oxidation number method. Both methods lead to the correct from of the balanced equation. The ion electron method has two advantages. So some chemists prefer to use the ion-electron method for redox reactions carried out in dilute aqueous solutions, where free ions have more or less independent existence The oxidation state method for redox reactions is mostly used for solid chemicals or for reactions in concentrated acid media For the reaction The -factor is
Redox equations are balanced either by ion-electron method or by oxidation number method. Both methods lead to the correct from of the balanced equation. The ion electron method has two advantages. So some chemists prefer to use the ion-electron method for redox reactions carried out in dilute aqueous solutions, where free ions have more or less independent existence The oxidation state method for redox reactions is mostly used for solid chemicals or for reactions in concentrated acid media For the reaction The -factor is
The valency of carbon is generally 4, but its oxidation state may be -4,-2,0,+2,-1 etc. In the compounds containing C,H, and O, the oxidation number of C is calculated as Oxidation number of Where
and nc are the number of oxygen, hydrogen and carbon atoms , respectively The oxidation state of C in diamond is
The valency of carbon is generally 4, but its oxidation state may be -4,-2,0,+2,-1 etc. In the compounds containing C,H, and O, the oxidation number of C is calculated as Oxidation number of Where
and nc are the number of oxygen, hydrogen and carbon atoms , respectively The oxidation state of C in diamond is
Oxidation reaction involves loss of electrons, and reduction reaction involves gain of electrons. The reaction in which a species disproportionate into two oxidation states (lower and higher) is called disproportionate reaction Which of the following statements is wrong?
Oxidation reaction involves loss of electrons, and reduction reaction involves gain of electrons. The reaction in which a species disproportionate into two oxidation states (lower and higher) is called disproportionate reaction Which of the following statements is wrong?
This section contains five paragraphs. Based on each paragraph, 3-7 multiple choice questions have to be answered. Each question has four choices (a) , (b) , (c) , and (d) , out of which only one is correct, except in the paragraph for problem 19-25 Consider the following unbalanced redox reaction:
The oxidation number of X is-2, and neither X nor water is involved in the redox process
The element(s) undergoing oxidation is/are
This section contains five paragraphs. Based on each paragraph, 3-7 multiple choice questions have to be answered. Each question has four choices (a) , (b) , (c) , and (d) , out of which only one is correct, except in the paragraph for problem 19-25 Consider the following unbalanced redox reaction:
The oxidation number of X is-2, and neither X nor water is involved in the redox process
The element(s) undergoing oxidation is/are
Statement 1: and
are both bleaching agents
Statement 2:Both are reducing agents
Statement 1: and
are both bleaching agents
Statement 2:Both are reducing agents
Statement 1:Reduction of 3-phenyl prop-2-en-1-al with LAH gives 3-phenyl prpan-1-ol
Statement 2:Both the double bond and the aldehyde group of unsaturated aldehydes are reduced by LAH
Statement 1:Reduction of 3-phenyl prop-2-en-1-al with LAH gives 3-phenyl prpan-1-ol
Statement 2:Both the double bond and the aldehyde group of unsaturated aldehydes are reduced by LAH
Statement 1:A reaction between Fe and I2 occurs, but a reaction between and
does not occur
Statement 2:Fe is a better reducing agent than
Statement 1:A reaction between Fe and I2 occurs, but a reaction between and
does not occur
Statement 2:Fe is a better reducing agent than