What is diffraction of light? Find the formula for the angular fringe width of the central maxima obtained in the diffraction pattern of monochromatic light by a single slit. Show the diagram of intensity distribution of light in the diffraction pattern.
Show Hint
The angular fringe width depends on the wavelength of the light and the width of the slit. Larger slits produce narrower fringes.
Step 1: Diffraction of Light.
Diffraction of light is the bending of light waves around the edges of obstacles and openings. When light passes through a narrow slit or around an obstacle, it spreads out and forms a diffraction pattern. The central maximum is the brightest region, and it is flanked by dark and bright fringes.
Step 2: Formula for Angular Fringe Width.
In the diffraction pattern produced by a single slit, the angular fringe width \( \beta \) (angular distance between adjacent dark fringes) is given by the formula:
\[
\beta = \frac{\lambda}{a}
\]
where:
- \( \lambda \) is the wavelength of the light,
- \( a \) is the width of the slit.
Step 3: Intensity Distribution.
The intensity distribution of light in the diffraction pattern from a single slit is given by:
\[
I(\theta) = I_0 \left( \frac{\sin \left( \frac{\pi a}{\lambda} \sin \theta \right)}{\frac{\pi a}{\lambda} \sin \theta} \right)^2
\]
where \( I_0 \) is the maximum intensity at the central maximum, \( \theta \) is the angle of diffraction, and \( a \) is the width of the slit.
Step 4: Diagram.
Here’s the diagram showing the intensity distribution of light in the diffraction pattern:
