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Estimate the linear separation of two objects on Mars that can just be resolved under ideal conditions by an observer on Earth (a) using the naked eye and (b) using the 200in.(=5.1m) Mount Palomar telescope. Use the following data: distance to Mars = 8.0107km, diameter of pupil = 5.0mm, wavelength of light 550nm.

Short Answer

Expert verified
  1. The linear separation of two objects on Mars is1.1104km .
  2. The linear separation of two objects on Mars is 11km.

Step by step solution

01

Introduction

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02

Calculation

Distance from the observer to the object

L=8107km=81010m

Wave length

=550nm=550nm10-9m/nm=55010-9m

Distance from the pupil eye

d=5mm=5mm10-3m/mm=510-3m

D is separation between objects.

03

(a) Find the linear separation of two objects on Mars

We have the conditiontanR=DL

And from criteria sinR=1.22d

As Ris small tanRsinRR

Therefore,

DL=1.22dD=1.22LdD=1.2281010m55010-9m510-3m=1073.6104m=1.1107m10-3km/m=1.1104km

Hence, the linear separation of two objects on Mars is 1.1104km.

04

(b) Find the linear separation of two objects on Mars

In this case d=5.1m;

D=1.2281010m55010-9m5.1m=1052.549101m=10525.49m10-3km/m=11km

Hence, the linear separation of two objects on Mars is 11km.

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