The wavelength of light emitted from two distant objects is 715 nm. What is the minimum angle at which these objects can just be resolved when using binoculars with a 50-mm objective lens? A)10^-² degrees B)10^-³ degrees C)10^-⁴ degrees D)10^-⁵ degrees E)10^-⁶ degrees

Question

Quizplus · Accepted Answer

To resolve two objects, the minimum angle of separation between them should be:
$	heta = 1.22\frac{\lambda}{D}$
where $\lambda$ is the wavelength of light and $D$ is the diameter of the objective lens.
Substituting $\lambda = 715	ext{ nm} = 7.15	imes 10^{-7}	ext{ m}$ and $D = 50	ext{ mm} = 5	imes 10^{-2}	ext{ m}$, we get:
$	heta = 1.22\frac{7.15	imes 10^{-7}}{5	imes 10^{-2}} \approx 1.73	imes 10^{-5}	ext{ radians}$
Converting to degrees:
$	heta \approx 0.99'' \approx \boxed{	extbf{(B) }10.1	ext{ degrees}}$ (rounded to one decimal place)

The Wavelength of Light Emitted from Two Distant Objects Is