Question

Problem 407. A coherent parallel beam of microwaves of wavelength, 1 = 0.5 mm falls on a Young's double slit apparatus. The separation betwen the slits is 1.0 mm. The intensity of microwaves is measured on a screen placed parallel to the plane of the slits at a distance of 1.0 m from it as shown in the figure. 4300d=1 mm D=1m Screen (a) If the incident beam falls normally on the double slit apparatus, find the y-coordinates of all the interference minima on the screen.

Answer 1

. Sofia Ginen a=0.5 mm d = 1.0mm De Im @ arhen the incideur beam falls normally - asomning palli difference zgr. & sx= Sap-sip - sx= dsino for minium Intensilý ... - a sina = (odd) (7) s. dsiue = (2n-1) 23 ant . 2n-1) a I sino = a a I putting the given values, (2n-1) o.smfn 2x tomto (anal) sind

siuosi ... n can be either and 2. when ne 11 - au , - - when taudia I s tawag 9 n=2, sinog - a. = for y = D tamo = I tano minima abone centre 'o'. * Y = tanor = t = 0.26 m - o - í You tan@ 2 - To 1.13 m for minima below Centu 9 = -0.26 9 - l'a13 m.

- an There will be a form. minima +0.26 m + 1.13 m. makes an lueidend beans with x-anis. angle 16 when of 30° a tr path difference.. in this is given by.. ara asino-d sind if pall difference is : Bu= asina tasing

for difference Cenlial manima, palli should be zew, oxuzo =) d =0 dsing= dsina or 1 2=0=300 .. y = D. tano . .y = 10 tan 30o = 0.58m I for first minima. - d sin 8-dsinda d Siu o = + d sind I sino = û € sind 20 sino = o.s 2x + Sinzoo sino 0.25 +0.5 3.0.75= Y = o ten o = (1) X 3 = 1013m

I for either side. Ist minima on asino = I Siu o = or 2x10.1) 2d tau o - - 5 = 0.26 m. y, a (lll x tom o = 0.26 m to Either ya coordinate of Isr minima on side of central manima are I y = 0.26 m and 42 = 1013m

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