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xz_007 [3.2K]
2 years ago
5

In a Young's double-slit experiment, 610-nm-wavelength light is sent through the slits. The intensity at an angle of 2.95° from

the central bright fringe is 85% of the maximum intensity on the screen. What is the spacing between the slits?
Physics
1 answer:
Sliva [168]2 years ago
7 0

Answer:

spacing between the slits is 405.32043 ×10^{-9}  m

Explanation:

Given data

wavelength = 610 nm

angle = 2.95°

central bright fringe = 85%

to find out

spacing between the slits

solution

we know that spacing between slit is

I = 4I_{0} × cos²∅/2

so

I/4I_{0}  = cos²∅/2

here I/4I_{0} is 85 % = 0.85

so

0.85 = cos²∅/2

cos∅/2 = √0.85

∅ = 2 ×cos^{-1} 0.921954

∅  = 45.56°

∅  = 45.56° ×π/180 = 0.7949 rad

and we know that here

∅  = 2π d sinθ / wavelength

so

d = ∅× wavelength /  ( 2π  sinθ )

put all value

d = 0.795 × 610×10^{-9} / ( 2π  sin2.95 )

d = 405.32043 ×10^{-9}  m

spacing between the slits is 405.32043 ×10^{-9}  m

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