Chapter 36: Q27P (page 1110)

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

Short Answer

Expert verified

The altitude using the angular separation formula is $1.6 \times 10^{3} km$ .

Step by step solution

Given data

Wavelength of x-Ray, $λ = 0.10 nm$

The pupil diameter $d = 4.00 mm$

The resolving separation $D = 5.0 cm$

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 $0.1 - 10$ Nanometers.

Determining the altitude using the angular separation formula

Let the altitude be 'L'

Since angular separation $ϕ_{R} = 1.22 \frac{λ}{d}$

But $ϕ_{R} = D/L$

So $D = \frac{1.22 λ L}{d}$

Or,

$L = \frac{D d}{1.22 λ} = \frac{5.0 \times 10^{- 2} m \times 4.0 \times 10^{- 3} m}{1.22 \times 0.10 \times 10^{- 9} m} = 1.639 \times 10^{6} m L = 1.6 \times 10^{3} km$

Hence, the altitude using the angular separation formula is $1.6 \times 10^{3} km$ .

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

Short Answer

Step by step solution

Given data

Definition of X-rays

Determining the altitude using the angular separation formula

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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

Step by step solution

Given data

Definition of X-rays

Determining the altitude using the angular separation formula

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Fluids

Electricity and Magnetism

Rotational Dynamics

Space Physics

Magnetism and Electromagnetic Induction

Force

Study anywhere. Anytime. Across all devices.

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