In a Young\'s interference experiment, the two slits are separatedby 0.13 mm and

Question

In a Young's interference experiment, the two slits are separatedby 0.13 mm and the incident light includestwo wavelengths: 1 = 540 nm (green) and2 = 450 nm (blue). The overlappinginterference patterns are observed on a screen 1.33 m from the slits. (a) Find a relationship between the ordersm1 and m2 that determineswhere a bright fringe of the green light coincides with a brightfringe of the blue light. (The order m1 isassociated with 1, andm2 is associated with2.)
m2/m1 = 1

(b) Find the minimum values of m1 andm2 such that the overlapping of the brightfringes will occur and find the position of the overlap on thescreen. m1 = 2 m2 = 3 Distance = 4 cm from the central maximum
(a) Find a relationship between the ordersm1 and m2 that determineswhere a bright fringe of the green light coincides with a brightfringe of the blue light. (The order m1 isassociated with 1, andm2 is associated with2.)
m2/m1 = 1

(b) Find the minimum values of m1 andm2 such that the overlapping of the brightfringes will occur and find the position of the overlap on thescreen. m1 = 2 m2 = 3 Distance = 4 cm from the central maximum m1 = 2 m2 = 3 Distance = 4 cm from the central maximum

Explanation / Answer

The condition to get constructive interference (ie, brightfringes) is   d sin = m , where sin =y / L . thus,   d y / L = m for brightfringes . For Blue:    d y / L = m2 (450) For Green:   d y / L = m1(540) for overlap of blue and green bright fringes, the two valuesof y are the SAME!!! divide the blue eqn above by the green eqn toget:     1 =   (450m2 ) / ( 540 m1 ) thus,   m2 / m1 = 540 / 450 = 1.2   this is our firstanswer. this ratio of m2 / m1 isalso equal to   2.4 / 2 or 2.6 / 3 or 4.8 / 4 or 6 /5. Bingo, we got integers and thus the minimum valuesare   m1 = 5   and m2 = 6.   these are the second andthird answers. The distance from the central max is y.   Since y is the same for both the blue and green, it does not matterwhich eqn we use to calculate y.    I will use thegreen eqn from above:                                                                                              d y / L =   ( 5) ( 540 nm ) solve for y  = (5) (540 nm) (1.33 m ) /( 0.133 mm )   be careful of the units here (changeeverything to meters). we get y = 0.027 meters or 2.7 cm   , this isthe fourth answer.

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