Diffraction Pattern of Light Passing through Single Slit

What is the largest slit width for which there are no minima in the diffraction pattern?

The largest slit width for which there are no minima in the diffraction pattern is determined by the wavelength of the light and the practical limitations of the experiment.

Answer:

The largest slit width for which there are no minima in the diffraction pattern is when the angle of diffraction is zero. In other words, the diffracted light should be in the same direction as the incident light.

When light passes through a single slit, it undergoes diffraction which causes interference patterns on a screen placed behind the slit. These patterns are characterized by maxima and minima, where the maxima represent bright fringes and the minima represent dark fringes.

The position of the minima is given by the equation: sinθ = m(λ/d) where θ is the angle of diffraction, m is the order of the minimum, λ is the wavelength of light, and d is the width of the slit.

For there to be no minima in the diffraction pattern, the value of sinθ should be zero. This means that the angle of diffraction should also be zero. In other words, the diffracted light should be in the same direction as the incident light.

If we substitute sinθ = 0 in the equation above, we get: m(λ/d) = 0

This equation implies that m can be any integer, but d cannot be zero. Therefore, the largest slit width for which there are no minima in the diffraction pattern is when m = 0, which means that the width of the slit should be large enough to allow all the light to pass through without diffracting.

However, we should also consider the practical limitations of the experiment. In reality, it is difficult to make a slit that is infinitely wide. Therefore, we can use a rule of thumb that states that the width of the slit should be at least 10 times the wavelength of the light. In our case, the wavelength of the helium-neon laser is 633 nm, so the largest slit width for which there are no minima in the diffraction pattern should be around 6.33 µm.