Two slits $$s1$$ and $$s2$$ are on a plane inclined at an angle of $$450$$ with horizontal. The distance between the slits is $$2$$ mm. A monochromatic point source S of wavelength λ$$=5000A0$$ is placed at a distance $$1/2$$ mm from the midpoint of slits as shown in figure. The screen is placed at a distance of $$2$$ m. The fringe width of interference pattern on the screen is $$n10mm$$. Find the integer closest to n

Question

Two slits $$s1$$ and $$s2$$ are on a plane inclined at an angle of $$450$$ with horizontal. The distance between the slits is $$2$$ mm. A monochromatic point source S of wavelength λ$$=5000A0$$ is placed at a distance $$1/2$$ mm from the midpoint of slits as shown in figure. The screen is placed at a distance of $$2$$ m. The fringe width of interference pattern on the screen is $$n10mm$$. Find the integer closest to n

Infinity Learn · Accepted Answer

For small angles,$$sin$$θ$$=$$θ and $$cos$$θ$$=1$$∠$$S1S2M=45-$$θΔ$$x1=dcos(45-$$θ$$)$$Δ$$x=$$Δ$$xi+dcos$$⁡(45$$−θ$$)Δ$$x=$$Δ$$xi+d($$$$cos$$⁡$$45cos$$⁡θ$$+$$$$sin$$⁡$$45sin$$⁡θ$$)$$Δ$$x=$$Δ$$xi+2$$×$$10$$−$$3121+12$$θ For central & first maxima Δx is $$0$$,λ∴$$0=$$Δ$$xi+2$$×$$10$$−$$312+12$$θ$$1$$λ$$=$$Δ$$xi+2$$×$$10$$−$$312+12$$θ$$2$$ Subtracting λ$$=2$$×$$10$$−$$312$$Δθ∵Δθ$$=$$β$$D5$$×$$10$$−$$7=10$$−$$3$$β$$2$$β$$=52$$×$$10$$−$$4$$β$$=5210mm=7.0710mm$$

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