(a) Assuming the fringes are laid out linearly along the screen, find the positi

Question

(a) Assuming the fringes are laid out linearly along the screen, find the position of the n = 50 fringe by multiplying the position of the n = 1 fringe by 50.0.
? m

(b) Find the tangent of the angle the first-order bright fringe makes with respect to the line extending from the point midway between the slits to the center of the central maximum.
?

(c) Using the result of part (b) and

dsin?bright = m?,

calculate the wavelength of the light.
? nm

(d) Compute the angle for the 50th-order bright fringe from

dsin?bright = m?.

?

Explanation / Answer

y bright = 4.5mm

but ybright = n*lamda*L/d...

here n= 1 for first order maximum
L = 1.7 m

and d= 2.15*10^-4 m..
lamda = (4.5*10^-3*2.15*10^-4)/1.7 = 569.12 nm..

for n= 50

ybright = 50*lamda*L/d = 50*4.5 = 225 mm...

B) tan theta = y bright/L = (4.5*10^-3)/1.7 = 0.151 degrees..

c) d*sin theta_bright = m*lamda..

lamda = d sin theta_bright = (2.15*10^-4)*sin(0.151) = 566.62 nm

d) d*sin theta_bright = m*lamda..

here m= 50....

theta_bright = sin^-1[(50*566.62*10^-9)/(2.15*10^-4)] = 7.57 degrees

e) Ybright = L*tan theta_bright..
ybright = 1.7*tan(7.57) = 0.225m = 225 mm

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