In bright light, the pupils of the eyes of a cat narrow to a...

In bright light, the pupils of the eyes of a cat narrow to a vertical slit $0.30 \mathrm{~mm}$ across. Suppose that a cat is looking at two mice $18 \mathrm{~m}$ away. What is the smallest distance between the mice for which the cat can tell that there are two mice rather than one using light of $560 \mathrm{~nm}$ ? Assume the resolution is limited by diffraction only.

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Key Concepts

Diffraction

Diffraction is the bending and spreading of waves when they pass through an aperture or around an obstacle. This phenomenon limits the resolution of any optical system because the waves interfere with each other, creating patterns (diffraction patterns) that can blur together closely spaced objects.

Angular Resolution

Angular resolution is the smallest angular separation between two objects that an optical system, such as an eye or telescope, can distinguish. It is fundamentally limited by diffraction and depends on both the wavelength of the light used and the size of the aperture through which the light is collected.

Rayleigh Criterion

The Rayleigh criterion defines the limit at which two point sources can be resolved—when the central maximum of one diffraction pattern coincides with the first minimum of the other. This criterion provides a practical measure of the resolution of an optical system and is used to determine the minimum resolvable angular separation.

Aperture and Wavelength Relationship

The relationship between the aperture size and the wavelength of light is central to determining the resolving power of an optical system. A larger aperture or a shorter wavelength reduces the effects of diffraction, thereby improving the system’s ability to distinguish between two closely spaced objects.

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