InterviewSolution
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InterviewSolution
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In a modified YDSE, sources `S` is kept in front of slit `S_(1)`. Find the phase difference at point O 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. A liquid of refractive index `mu` is filled between the screen and slits.A. `(2pi)/(lambda) = [[ sqrt(d^(2) + x_(0)^(2)) + x_(0)] + (mu d^(2))/(2D)]`B. `(2pi)/(lambda) = [[ sqrt(d^(2) + x_(0)^(2)) - x_(0)] + (mu d^(2))/(2D)]`C. `(2pi)/(lambda) = [[ sqrt(d^(2) - x_(0)^(2)) + x_(0)] + (mu d^(2))/(2D)]`D. `(2pi)/(lambda) = [[ sqrt(d^(2) - x_(0)^(2)) - x_(0)] + (mu d^(2))/(2D)]` |
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Answer» Correct Answer - b While calculating path difference, it must be remembered that is is equal to difference of optical path lengths from sources S to point on the screen. `:. Delta x_("total") = [Delta x]_("before slits") + [Delta x]_("after slits")` ` = (SS_(2) - SS_(1)) + (S_(2) P - S_(1) P)` ltbgt a. When liquid is filled between the slits and screen, then `[S_(2) P]_("liquid") = [mu S_(2) P]_("air")` `[S_(1) P]_("liquid") = [mu S_(1) P]_("air")` At point O: `mu S_(2) O = mu S_(1) O` Noth path difference is introduced after slits. So, `Delta x_("total") = SS_(2) - SS_(1) = sqrt(d^(2) + X_(0)^(2)) - x_(0)` Thus, phase diffenence, `Delta phi = (2pi)/(lambda) (sqrt(d^(2) + X_(0)^(2)) - x_(0))` At point P: `[Delta x]_("before slits") = sqrt(d^(2) + x_(0)^(2)) - x_(0)` `[Delta x]_("after slits") = mu S_(2) P - mu S_(1) ap = mu (S_(2)P - S_(1)P)` `= (mu yd)/(D) = (mu d^(2))/(2 D) ("as" y = (d)/(2))` Thus phase difference, `Delta phi = (2pi)/(lambda) [(sqrt(d^(2) + x_(0)^(2)) - x_(0)) + (mu d^(2))/(2 D)]` b. When liquid is filled between the source and slits: At point O: `(Delta x)_("before slits") = (SS_(2) + SS_(1))_("liquid")` `(mu SS_(2) + mu SS_(1))_("air")` `= mu (sqrt(d^(2) + x_(0)^(2)) - x_(0))` `(Delta x)_("after slits") = S_(2) O + S_(1) O = 0` `(Delta x)_("total") = mu (sqrt(d^(2) + x_(0)^(2)) - x_(0))` Thus, phase differnce at P, ` Delta phi = (2pi)/(lambda) (mu sqrt(d^(2) + x_(0)^(2)) - x_(0))` At point P: `(Delta x)_("before slits") = (SS_(2) + SS_(1))_("liquid") = (mu SS_(2) + mu SS_(1))_("air")` `(Delta x)_("after slits") = (S_(2)P - S_(1)P)_("air") = (y d)/(D) = (d^(2))/(2D)` `(Delta x)_("total") = [(mu sqrt(d^(2) + x_(0)^(2)) - x_(0)) + (d^(2))/(2D)]` Thus, phase difference at P, `Delta phi = (2 pi)/(lambda) [mu sqrt(D^(2) + x_(0)^(2)) - x_(0) + (d^(2))/(2D)]` |
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