DOe DARe!/T 2818 11:39:00 PM End Date: 4/13/2018 4:0000 AM (696) Problem II: The
ID: 2039743 • Letter: D
Question
DOe DARe!/T 2818 11:39:00 PM End Date: 4/13/2018 4:0000 AM (696) Problem II: The figure shows a double slit located a distance x-1.9 m from a screen, with the distance from the center of the screen to a bright fringe given by y. When the distance d between the slits is large compared to the wavelength , there will be numerous such bright fringes Screen view Ctheexpertta.com Find the wavelength of light, in nanometers, that produces fringes 7.5 mm apart on a sereen 1.9 m from double slits separated by 0.11 mm 0.434 10-5 You may assume that the angle 8 is small. Grade Summary Potential Submissions 90% Attempts remaining 10 cotan asin acos4 5 6 atan acotanO % per attempt) etailed view sinh0 5% 5% coshO tanh cotanhO Degrees Radians END BACKSPACECLEAR Submit Hint Feedback I give up Hints:--deduction per hint. Hints remaining- Feedback: 4 deduction per feedback.Explanation / Answer
as we know,
distance of mth order fringe from central bright location is given by m*lambda*D/d
where lambda=wavelength
D=distance between the slits and the screen
d=slit width
so gap between neighbouring fringes=(m*lambda*D/d)-((m-1)*lambda*D/d)=lambda*D/d
as here D=distance of screen from slits=x
fringe gap=lambda*x/d
given fringe gap=7.5 mm=7.5*0.001 m
x=1.9 m
d=0.11 mm=0.11*10^(-3) m
then wavelength=lambda=fringe gap*d/x
=7.5*0.001*0.11*10^(-3)/1.9
=4.3421*10^(-7) m
=434.21 nm
as the answer is required in nanometers, correct answer will be 434.21
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