Shorter wavelengths can improve resolution because they allow for finer details to be resolved or distinguished. The resolution of a system refers to its ability to distinguish between two closely spaced objects or features. In the context of optics, resolution is often associated with the ability to resolve fine details in an image or distinguish closely positioned objects.
The resolution of an imaging system is determined by the diffraction limit, which is governed by the properties of waves. When light waves pass through a small aperture or encounter an obstacle, they diffract, spreading out and interfering with each other. This diffraction phenomenon limits the ability to distinguish fine details in an image.
The diffraction pattern produced by a wave passing through an aperture or encountering an obstacle depends on the wavelength of the wave. According to the Rayleigh criterion, which is commonly used to quantify resolution, two objects can be resolved if the peak of the diffraction pattern of one object falls on the first minimum (dark fringe) of the diffraction pattern of the other object.
The Rayleigh criterion can be expressed mathematically as:
θ = 1.22 * λ / D
where θ is the angular resolution, λ is the wavelength of the wave, and D is the size of the aperture or the diameter of the objective lens.
From this equation, it can be observed that as the wavelength (λ) decreases, the angular resolution (θ) improves. In other words, shorter wavelengths allow for smaller angular separations between objects to be resolved.
In practical terms, this means that imaging systems that operate with shorter wavelengths, such as X-rays or electron microscopes, can achieve higher resolution and resolve finer details compared to systems that operate with longer wavelengths, such as visible light. This principle is utilized in various fields, including microscopy, astronomy, and particle physics, where high-resolution imaging is crucial for studying intricate structures and phenomena.