The headlights of a car emit light of wavelength 400 nm and are separated by 1.2 m. The headlights are viewed by an observer whose eye has an aperture of 4.0 mm. The observer can just distinguish the headlights as separate images. What is the distance between the observer and the headlights?

A. 8 km

B. 10 km

C. 15 km

D. 20 km

Light is incident on a diffraction grating. The wavelengths of two spectral lines of the light differ by $0.59 \mathrm{nm}$ and have a mean wavelength of $590 \mathrm{nm}$. The spectral lines are just resolved in the fourth order of the grating. What is the minimum number of grating lines that were illuminated?

A.  $25$

B.  $250$

C.  $1000$

D.  $4000$

Estimate, in rad, the smallest angular separation of two distinct point sources of light of wavelength 656 nm that can be resolved by the eye of this observer.

The light illuminates a width of 3.5 mm of the grating. The deuterium and hydrogen red lines can just be resolved in the second-order spectrum of the diffraction grating. Show that the grating spacing of the diffraction grating is about 2 × 10^–6m.

The yellow light is made from two very similar wavelengths that produce two lines in the spectrum of sodium. The wavelengths are 588.995 nm and 589.592 nm. These two lines can just be resolved in the second-order spectrum of this diffraction grating. Determine the beam width of the light incident on the diffraction grating.

The painting contains a pattern of red dots with a spacing of 3 mm. Assume the wavelength of red light is 700 nm. The average diameter of the pupil of a human eye is 4 mm. Calculate the maximum possible distance at which these red dots are distinguished.

Airports use radar to track the position of aircraft. The waves are reflected from the aircraft and detected by a large circular receiver. The receiver must be able to resolve the radar images of two aircraft flying close to each other.

The following data are available.

Calculate the minimum distance between the two aircraft when their images can just be resolved.

An observer with an eye of pupil diameter $d$ views the headlights of a car that emit light of wavelength $\lambda$. The distance between the headlights is $L$.

What is the greatest distance between the observer and the car at which the images of the headlights will be resolved by the observer’s eye?

A.  $\frac{1.22\lambda }{Ld}$

B.  $\frac{1.22\lambda L}{d}$

C.  $\frac{Ld}{1.22\lambda }$

D.  $\frac{d}{1.22\lambda L}$