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Physics for Scientists and Enginee...

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

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BuyFindarrow_forward

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 250km . The average wavelength is 500nm . The pupil diameter of the astronaut is 5mm .

The condition required for the image resolution is,

θmin=1.22λD (1)

Here;

θmin is the limiting angle of resolution.

λ is the wavelength.

D is the diameter of pupil.

Substitute 500nm for λ and 5mm for D in equation (1)

θmin=1.22((500nm×(1m109nm))5mm×(1m103mm))=1.22×104radian

The value of the limiting angle is 1.22×104radian .

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

tanθmin=dminL (2)

Here,

dmin is the size of the smallest object

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