p37_015.pdf

15. (a) We use the Rayleigh criteria. Thus, the angular separation (in radians) of the sources must be

at least θ R =1 . 22 λ/d ,where λ is the wavelength and d is the diameter of the aperture. For the

headlights of this problem,

θ R = 1 . 22(550

10 − 9 m)

=1 . 34

10 − 4 rad .

5 . 0

10 − 3 m

(b) If L is the distance from the headlights to the eye when the headlights are just resolvable and D

is the separation of the headlights, then D = Lθ R , where the small angle approximation is made.

This is valid for θ R in radians. Thus,

L = D

1 . 4m

10 − 4 rad =1 . 0

10 4 m=10km .

1 . 34

θ R =