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Physics-

General

Easy

Question

In an interfrence arrangement similar to Young's double- slit experiment, the slits $S subscript 1 end subscript & S subscript 2 end subscript$ are illuminated with coherent microwave sources, each of frequency 106 Hz. The sources are synchronized to have zero phase difference. The slits are separated by a distance d = 150.0 m and screen is at very large distance from slits. The intensity I(q) is measured as a function of $theta$ , where $theta$ is defined as shown. Screen is at a large distance. If $I subscript 0 end subscript$ is the maximum intensity then I ( $theta$ ) for $0 less or equal than theta less or equal than 90 to the power of ring operator end exponent$ is given by:

$I (θ) = 1_{d} / 2 for θ = 30^{\circ}$
$l (θ) = I / 4 for θ = 90^{\circ}$
$I (θ) = I_{0} for θ = 0^{\circ}$
I( $θ$ ) is constant for all values of $θ$

The correct answer is: $I left parenthesis theta right parenthesis equals I subscript 0 end subscript text for end text theta equals 0 to the power of ring operator end exponent$

The intensity of light is I(q)= $I subscript 0 end subscript cos to the power of 2 end exponent invisible function application open parentheses fraction numerator delta over denominator 2 end fraction close parentheses$
$delta equals fraction numerator 2 pi over denominator lambda end fraction open parentheses capital delta x close parentheses equals open parentheses fraction numerator 2 pi over denominator lambda end fraction close parentheses open parentheses dsin invisible function application theta close parentheses$
(i) For q = 30°
$table row cell lambda equals fraction numerator c over denominator v end fraction equals fraction numerator 3 cross times 10 to the power of 8 end exponent over denominator 10 to the power of 6 end exponent end fraction equals 300 m text end text text a end text text n end text text d end text text end text d equals 150 m end cell row cell delta equals open parentheses fraction numerator 2 pi over denominator 300 end fraction close parentheses left parenthesis 150 right parenthesis open parentheses fraction numerator 1 over denominator 2 end fraction close parentheses equals fraction numerator pi over denominator 2 end fraction therefore fraction numerator delta over denominator 2 end fraction equals fraction numerator pi over denominator 4 end fraction end cell row cell therefore I open parentheses theta close parentheses equals I subscript 0 end subscript cos to the power of 2 end exponent invisible function application open parentheses fraction numerator pi over denominator 4 end fraction close parentheses equals fraction numerator I subscript 0 end subscript over denominator 2 end fraction end cell end table$
(ii) For $theta equals 90 to the power of ring operator end exponent$
$delta equals open parentheses fraction numerator 2 pi over denominator 300 end fraction close parentheses left parenthesis 150 right parenthesis left parenthesis A right parenthesis equals pi rightwards double arrow fraction numerator delta over denominator 2 end fraction equals fraction numerator pi over denominator 2 end fraction text and end text I left parenthesis theta right parenthesis equals 0$

Related Questions to study

In an interfrence arrangement similar to Young's double- slit experiment, the slits $S subscript 1 end subscript & S subscript 2 end subscript$ are illuminated with coherent microwave sources, each of frequency 106 Hz. The sources are synchronized to have zero phase difference. The slits are separated by a distance d = 150.0 m and screen is at very large distance from slits. The intensity I(q) is measured as a function of $theta$ , where $theta$ is defined as shown. Screen is at a large distance. If $I subscript 0 end subscript$ is the maximum intensity then I ( $theta$ ) for $0 less or equal than theta less or equal than 90 to the power of ring operator end exponent$ is given by:

In an interfrence arrangement similar to Young's double- slit experiment, the slits $S subscript 1 end subscript & S subscript 2 end subscript$ are illuminated with coherent microwave sources, each of frequency 106 Hz. The sources are synchronized to have zero phase difference. The slits are separated by a distance d = 150.0 m and screen is at very large distance from slits. The intensity I(q) is measured as a function of $theta$ , where $theta$ is defined as shown. Screen is at a large distance. If $I subscript 0 end subscript$ is the maximum intensity then I ( $theta$ ) for $0 less or equal than theta less or equal than 90 to the power of ring operator end exponent$ is given by:

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A parallel beam of light $left parenthesis lambda equals 5000 text Å end text right parenthesis$ is incident at an angle $alpha equals 30 to the power of ring operator end exponent$ with the normal to the slit plane in a young’s double slit experiment. Assume that the intensity due to each slit at any point on the screen is $I subscript 0 end subscript$ . Point O is equidistant from $S subscript 1 end subscript & S subscript 2 end subscript$ . The distance between slits is 1mm.

A parallel beam of light $left parenthesis lambda equals 5000 text Å end text right parenthesis$ is incident at an angle $alpha equals 30 to the power of ring operator end exponent$ with the normal to the slit plane in a young’s double slit experiment. Assume that the intensity due to each slit at any point on the screen is $I subscript 0 end subscript$ . Point O is equidistant from $S subscript 1 end subscript & S subscript 2 end subscript$ . The distance between slits is 1mm.

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