No, a microscope cannot see smaller objects if it uses a higher wavelength of light. In fact, the resolution of an optical microscope is fundamentally limited by the diffraction of light, which is dependent on the wavelength of the light being used.
The resolution of a microscope refers to its ability to distinguish two closely spaced objects as separate entities. According to the Rayleigh criterion, the smallest resolvable detail (d) in an image is given by the equation:
d = 1.22 * (λ / NA)
where λ is the wavelength of light and NA is the numerical aperture of the microscope's objective lens.
From this equation, it can be observed that as the wavelength of light (λ) increases, the resolution (d) also increases. In other words, a higher wavelength of light leads to reduced ability to resolve smaller details.
To visualize smaller objects, a microscope with a shorter wavelength of light is desirable. This is why electron microscopes, which use beams of electrons instead of light, can achieve much higher resolution than optical microscopes. Electrons have much smaller wavelengths compared to visible light photons, allowing electron microscopes to resolve much finer details.
In summary, the resolution of a microscope is inversely proportional to the wavelength of light used. Higher wavelength light reduces the microscope's ability to see smaller objects clearly.