A camera lens having a 50-mm focal length is set to f/4.0. What is the minimum spacing of two objects located 12 m from the lens if the objects are just barely resolved in the image using light of
Wavelength 500 nm?
A) $0.59 \mathrm {~mm}$
B) $4.72 \mathrm {~mm}$
C) $0.024 \mathrm {~mm}$
D) $1.66 \mathrm {~mm}$
E) $4.9 \times 10 ^ { - 5 } \mathrm {~m}$

Question

A camera lens having a 50-mm focal length is set to f/4.0. What is the minimum spacing of two objects located 12 m from the lens if the objects are just barely resolved in the image using light of
Wavelength 500 nm? 
A) $0.59 \mathrm {~mm}$
B) $4.72 \mathrm {~mm}$
C) $0.024 \mathrm {~mm}$
D) $1.66 \mathrm {~mm}$
E) $4.9 \times 10 ^ { - 5 } \mathrm {~m}$

Quizplus · Accepted Answer

The minimum spacing of two objects for them to be just barely resolved, according to the Rayleigh criterion, can be calculated using the formula $d = 1.22 \frac{f \lambda}{D}$, where $f$ is the focal length of the lens, $\lambda$ is the wavelength of light, and $D$ is the diameter of the lens aperture. Given $f = 50$ mm, $\lambda = 500$ nm = $500 \times 10^{-6}$ mm, and the f-number $f/4.0$ which gives $D = \frac{f}{4.0} = 12.5$ mm, substituting these values into the formula gives a minimum spacing $d$ that matches choice A, $0.59$ mm.

A Camera Lens Having a 50-Mm Focal Length Is Set 0.59 mm0.59 \mathrm {~mm}0.59 mm

A Camera Lens Having a 50-Mm Focal Length Is Set $0.59 \mathrm {~mm}$