What,approximately,are the dimensions of the smallest object on Earth that the astronauts can resolve by eye at 200 km height from the space shuttle? Assume $\lambda$ = 500 nm light and a pupil diameter D = 0.50 cm.Assume eye fluid has an average n = 1.33.
A)150 m
B)100 m
C)250 m
D)25 m
E)18 m

Question

Quizplus · Accepted Answer

The smallest resolvable angle can be calculated by using the Rayleigh criterion: 
θ = 1.22(λ/D) where θ is the angle, λ is the wavelength of light, and D is the diameter of the pupil. 
Substituting the given values, we get: 
θ = 1.22(500 nm/0.50 cm) = 0.61 arc minutes 
At a height of 200 km, 1 arc minute corresponds to a distance of approximately 1.88 km. Therefore, the smallest resolvable distance is given by: 
d = θ × (200 km/1.88 km) = 64.6 m 
However, this is the theoretical limit and the actual size of the smallest object that can be resolved may vary due to other factors such as atmospheric distortion. Therefore, the closest option to the calculated value is E) 18 m.

What,approximately,are the Dimensions of the Smallest Object on Earth That λ\lambdaλ

What,approximately,are the Dimensions of the Smallest Object on Earth That $\lambda$