Consider the two-slit interference experiment. Electromagnetic radiation passes through the two slits that are a distance of 0.0170 nm apart. A fourth-order bright fringe forms at an angle of 8.0 degrees relative to the incident beam. What is the wavelength of the light?
1. 581 nm
2. 789 nm
3. 591 nm
4. 420 nm
To solve this problem, we can use the equation for the position of the bright fringes in a double-slit interference pattern:
d*sin(theta) = m*lambda
Where:
d = distance between the two slits = 0.0170 nm = 1.70 x 10^-8 m
theta = angle of the bright fringe = 8.0 degrees = 0.139 radians
m = order of the bright fringe = 4
lambda = wavelength of the light
Plugging in the given values:
1.70 x 10^-8 m * sin(0.139) = 4 * lambda
lambda = (1.70 x 10^-8 m * sin(0.139)) / 4
lambda = 5.91 x 10^-8 m
Converting this to nm:
lambda = 591 nm
Therefore, the answer is:
3. 591 nm