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In a typical young's double slit experim...


In a typical young's double slit experiment a point source of monochromatic light is kept as shown in the figure. If the source is given an instantaneous velocity v=1 mm per second towards the screen, then the instantaneous velocity of central maxima is given as `alphaxx10^(-beta)cm//s` upward in scientific notation find the value of `alpha+beta`

Text Solution

Verified by Experts


The central maxima `(dy)/(D)=sqrt(d^(2)+x^(2))-x=x[1+(d^(2))/(2x^(2))]-x=(d^(2))/(2x)`
`y=(Dd)/(2x)implies(dy)/(dt)=-(Dd)/(2x^(2))((dx)/(dt))=((1xx0.01)/(2xx0.5xx0.5))xx(0.001)=0.02mm//s`
`impliesy=2xx10^(-3)cm//simpliesalpha+beta=5`
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Knowledge Check

  • In Young's double slit experiment, the slits are horizontal. The intensity at a point P as shown in figure is (3)/(4) I_(0) ,where I_(0) is the maximum intensity. Then the value of theta is, (Given the distance between the two slits S_(1) and S_(2) is 2 lambda )

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  • A monochromatic beam of light falls on Young's double slit experiment apparatus as shown in figure. A thin sheet of glass is inserted in front of lower slit S_(2) (lambda = 600 nm is wavelength of source) The phase difference between central masxima and 5th minima is

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  • In a modified Young's double-slit experiment, source S is kept in front of slit S_(1) as shown in the following figure. Find the phase difference at a point that is equidistant from slits S_(1) and S_(2) and point P that is in front of slit S_(1) in the following situations: If a liquid is filled between the slit and the source S, what is the phase difference?

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    `(2pi)/(lambda)[nsqrt(d^(2)+x_(0)^(2))+x_(0)+(d^(2))/(2D)]`
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    `(2pi)/(lambda)[nsqrt(d^(2)-x_(0)^(2))-x_(0)-(d^(2))/(2D)]`
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