In a two-slit experiment,the slit separation is 3.00 × m.The interference pattern is recorded on a flat screen-like detector that is 2.00 m away from the slits.If the seventh bright fringe on the detector is 10.0 cm away from the central fringe,what is the wavelength of the light passing through the slits?
A) 100 nm
B) 204 nm
C) 214 nm
D) 224 nm
E) 234 nm

Question

In a two-slit experiment,the slit separation is 3.00 ×  m.The interference pattern is recorded on a flat screen-like detector that is 2.00 m away from the slits.If the seventh bright fringe on the detector is 10.0 cm away from the central fringe,what is the wavelength of the light passing through the slits?
A) 100 nm 
B) 204 nm 
C) 214 nm 
D) 224 nm 
E) 234 nm

Quizplus · Accepted Answer

We can use the following formula for the location of the bright fringes on the screen:
y = mλL/d
where y is the distance from the central fringe to the mth bright fringe, λ is the wavelength of the light, L is the distance from the slits to the screen, d is the slit separation, and m is the order of the bright fringe.

In this case, we are given y = 10.0 cm = 0.100 m, L = 2.00 m, d = 3.00 × 10^(-6) m, and m = 7. Solving for λ, we get:
λ = yd/(mL) = (0.100 m)(3.00 × 10^(-6) m)/(7)(2.00 m) = 2.14 × 10^(-7) m = 214 nm

Therefore, the best choice is C, with a wavelength of 214 nm.

In a Two-Slit Experiment,the Slit Separation Is 3