Two stars are 10 light years away from the earth.  They are seen through a telescope of objective diameter 30 cm.  The wavelength of light is 600 nm.  To see the stars just resolved by the telescope, the minimum distance between them should be (1 light year = 9.46 × 1015m) of the order of :

  • Option 1)

    106 km

  • Option 2)

    108 km

  • Option 3)

    1011 km

  • Option 4)

    1010 km

 

Answers (1)

As we learnt in

Astronomical Telescope -

m= \frac{-f_{o}}{f_{e}}\left ( 1+\frac{f_{e}}{D} \right )
 

- wherein

f_{o} = focal length of objective

f_{e}= focal length of eyepiece

 

 Here \lambda=600\ nm=6\times 10^{-7}m

    \Delta = 30\ cm = 30\times 10^{-2}m=0.3 m

    R=10 log=10\times 9.46\times 10^{15}m

    l=?

Resolution of a telescope

\Delta \theta=\frac{1.22\lambda}{\Delta}\frac{l}{R}

\Rightarrow\ \; \frac{1.22\times 6\times 10^{-7}\times 10\times 9.46\times 10^{15}}{0.3}=2.31\times10^{8}\ km

Correct optio is 2.

 

 


Option 1)

106 km

This is an incorrect option.

Option 2)

108 km

This is the correct option.

Option 3)

1011 km

This is an incorrect option.

Option 4)

1010 km

This is an incorrect option.

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