The Mystery of the Helium-Neon Laser Diffraction Pattern
How can the width of a slit be determined using a helium-neon laser diffraction pattern?
A helium-neon laser with a wavelength of 633 nm illuminates a single slit and creates a diffraction pattern on a screen 1.50 m behind the slit. The distance between the first and second minima in the pattern is 4.75 mm. What is the width of the slit?
Answer:
The width of the slit can be calculated by using the formula [tex]Y = \frac{m\lambda * D}{d}[/tex] where m represents the order of the minimum, λ is the wavelength of the light, D is the distance between the screen and the slit, and d represents the width of the slit.
To determine the width of the slit, we can use the equations for the first and second minima in the diffraction pattern:
For the first minima: [tex]y_1 = \frac{1 * 633 * 10^{-9} * 1.5}{d}[/tex]
For the second minima: [tex]y_2 = \frac{2 * 633 * 10^{-9} * 1.5}{d}[/tex]
Given that the difference between the first and second minima is 4.75 mm, we have: [tex]y_2 - y_1 = 0.00475 m[/tex]
Solving for the width of the slit (d): [tex]\frac{633 * 10^{-9} * 1.5}{d} = 0.00475[/tex] [d = 0.0002 m or 0.2 mm]