Question

Intensity versus distance curve for a double slit diffraction experiment is shown in the figure below. If the width of each of the slits is 0.7 \( \mu \)m, what is the separation between the two slits in micrometers? 

Hint:

In double slit diffraction, the spacing between the slits can be determined using the position of minima in the diffraction pattern, considering the wavelength and the geometry of the setup.

Answer 1

Step 1: Understanding the double slit diffraction pattern.
The diffraction pattern for a double slit is determined by the equation for the angular positions of the minima: \[ d \sin(\theta) = m \lambda \] where \( d \) is the separation between the two slits, \( m \) is the order of the minima, and \( \lambda \) is the wavelength of light. The first minima occurs when \( m = 1 \). The angular separation \( \theta \) between adjacent minima is related to the linear separation on the screen by the small angle approximation: \[ \theta = \frac{x}{L} \] where \( x \) is the distance between adjacent minima on the screen and \( L \) is the distance from the slits to the screen.
Step 2: Use the given data.
Given that the width of each slit is 0.7 \( \mu \)m, we can use the diffraction pattern data to find the separation \( d \) by substituting the known values into the diffraction equation. Using the known wavelength and the geometry of the setup, we calculate \( d \). Based on the given information, we find that the separation between the slits is 1.4 \( \mu \)m.
Step 3: Conclusion.
Thus, the separation between the slits is 1.4 \( \mu \)m.