The head light of a jeep are 1.2 m apart. If the pupil of the eye of an observer has a diameter

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The head light of a jeep are 1.2 m apart. If the pupil of...

The head light of a jeep are $1.2 \mathrm{~m}$ apart. If the pupil of the eye of an observer has a diameter of $2 \mathrm{~mm}$ and light of wavelength $5896 \AA$ is used what should be the maximum distance of the jeep from the observer if two head lights are just seem to be separated apart? (A) $30.9 \mathrm{~km}$ (B) $33.4 \mathrm{~km}$ (C) $3.34 \mathrm{~km}$ (D) $30.9 \mathrm{~km}$

The head light of a jeep are $1.2 \mathrm{~m}$ apart. If the pupil of the eye of an observer has a diameter of $2 \mathrm{~mm}$ and light of wavelength $5896 \AA$ is used what should be the maximum distance of the jeep from the observer if two head lights are just seem to be separated apart?
(A) $30.9 \mathrm{~km}$
(B) $33.4 \mathrm{~km}$
(C) $3.34 \mathrm{~km}$
(D) $30.9 \mathrm{~km}$

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Key Concepts

Diffraction

Diffraction is the bending of waves around obstacles and through small apertures. In optics, diffraction limits the resolution of imaging systems because even a perfect lens cannot produce an infinitely sharp image, as the light spreads out after passing through an aperture.

Rayleigh Criterion

The Rayleigh criterion provides a way to quantify the minimum angular separation at which two point sources can be distinguished. It states that two sources are resolvable when the principal maximum of the diffraction pattern from one source coincides with the first minimum of the other.

Aperture Limitations

Optical systems, including the human eye, have apertures that restrict the amount of light that can enter, creating a diffraction effect. The diameter of the aperture, combined with the wavelength of light, determines the system's angular resolution, which limits how finely details can be resolved at a distance.

Angular Resolution and Geometric Projection

Angular resolution is the smallest angular separation between two objects that can be distinguished by an optical instrument. When determining the distance at which two objects can be resolved, their physical separation and this angular resolution are used together in a geometric projection, linking the observable angular separation to the actual distance between objects.

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