Chapter 37, Problem 11P

### Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
ISBN: 9781337553278

Chapter
Section

### Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
ISBN: 9781337553278
Textbook Problem

# What is the approximate size of the smallest object on the Earth that astronauts can resolve by eye when they are orbiting 250 km above the Earth? Assume λ = 500 nm and a pupil diameter of 5.00 mm.

To determine
The size of the smallest object that can be resolved by astronauts from satellite.

Explanation

Given Info: The distance between the astronauts in orbit and object on earth surface is 250â€‰km . The average wavelength is 500â€‰nm . The pupil diameter of the astronaut is 5â€‰mm .

The condition required for the image resolution is,

Î¸min=1.22Î»D (1)

Here;

Î¸min is the limiting angle of resolution.

Î» is the wavelength.

D is the diameter of pupil.

Substitute 500â€‰nm for Î» and 5â€‰mm for D in equation (1)

The value of the limiting angle is 1.22Ã—10âˆ’4â€‰radian .

The formula to calculate the minimum distance between the for image resolution is,

tanÎ¸min=dminL (2)

Here,

dmin is the size of the smallest object

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