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If Superman really had x-ray vision at 0.10nm wavelength and a 4.0mm pupil diameter, at what maximum altitude could he distinguish villains from heroes, assuming that he needs to resolve points separated by 5.0cm to do this?

Short Answer

Expert verified

The altitude using the angular separation formula is 1.6×103km.

Step by step solution

01

Given data

Wavelength of x-Ray,λ=0.10nm

The pupil diameter d=4.00mm

The resolving separation D=5.0cm

02

Definition of X-rays

X-rays is defined as the form of electromagnetic radiation, similar to light but of shorter wavelength and capable of penetrating solids and of ionizing gases. Such radiation having wavelengths in the range of approximately 0.1-10Nanometers.

03

Determining the altitude using the angular separation formula

Let the altitude be 'L'

Since angular separation ϕR= 1.22λd

But ϕR=D/L

So D=1.22λLd

Or,

L=Dd1.22λ=5.0×10-2m×4.0×10-3m1.22×0.10×10-9m=1.639×106mL=1.6×103km

Hence, the altitude using the angular separation formula is 1.6×103km.

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