In a single slit diffraction experiment, the width of the slit is 3.1 × 10^-5 m and the distance from the slit to the screen is 2.2 m. If the beam of light of wavelength 600 nm passes through the slit and forms a diffraction pattern on the screen, what is the linear distance on the screen from the center of the diffraction pattern to the first dark fringe? A) 2.1 cm B) 4.3 cm C) 6.3 cm D) 7.4 cm E) 8.5 cm

Question

Quizplus · Accepted Answer

We can use the formula for the location of the first minimum in a single slit diffraction pattern:

sin(θ) = λ / (wavelength)

where θ is the angle between the central maximum and the minimum, and λ is the wavelength. For small angles (which is true for this problem), we can approximate sin(θ) = θ. Rearranging the formula, we get:

θ = λ / (wavelength * width of slit)

The distance from the center of the pattern to the first minimum on the screen is given by:

L = distance to screen * tan(θ)

Substituting the given values, we get:

θ = (600 nm) / (3.1 × 10^-5 m) = 0.0192 radians

L = (2.2 m) * tan(0.0192) = 0.043 m = 4.3 cm

Therefore, the answer is B) 4.3 cm.

In a Single Slit Diffraction Experiment, the Width of the Slit