When two waveguides with identical cross-sectional areas but differing numerical apertures, NA₁ and NA₂ (where NA₂ is smaller than NA₁), are connected end-to-end, the resulting numerical aperture of the system is:

(NA₁ × NA₂) / (NA₁ + NA₂)
NA₁ + NA₂
NA₁
NA₂

Correct answer: NA₂

Solution

The numerical aperture of the system is determined by the waveguide with the smaller NA, as it limits the acceptance angle of light. Thus, the resulting numerical aperture is NA₂.

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