Question

The two headlights of an approaching automobile are 1.22 m apart. At what maximum distance will eye resolve them? Assume a pupil diameter of 5.0 mm & $\lambda$= 5500 A.U. Assume also that this distance is determined only by diffraction effect at the circular apperature

• A. 11 km
  
• B. 9.9 km
  
• C. 13 km
  
• D. 14 Km
  

Answer 1

The correct option is B 9.9 km

Aperture of pupil $d=5mmk\lambda =5500\mathring{A}$

The angular resolving power for eye in given by :-

${\theta }_{RP}=\frac{1.22\lambda }{d}\to \left(1\right)$

If headlights are $l=1.22m$ apart and a distance of ${}^{\prime }{o}^{\prime }$ from

${\theta }_{RP}=\frac{L}{D}\to \left(2\right)$ (angle subtended by two headlights )

From $\left(1\right)$ & $\left(2\right)$

$\frac{1.22\lambda }{d}=\frac{L}{D}\Rightarrow \frac{1.22\times 5.5\times {10}^{-7}}{5\times {10}^{-3}}=\frac{1.22}{D}$

$\Rightarrow D=9.9\times {10}^3=9.9km$