(a) Draw a neat labelled ray diagram showing the image formation of a distant object by a refracting telescope.
Deduce the expression for its magnifying power when the final image is formed at infinity.
(b) The sum of focal lengths of the two lenses of a refracting telescope is 105 cm. The focal length of one lens is 20 times that of the other. Determine the total magnification of the telescope when the final image is formed at infinity.

Explanation

(i)
Derivation `:`
Magnifying Power,
`M = ( tan beta )/( tan alpha) ~= (beta)/( alpha)`
Final image is formed at infinity when the image A.B. is formed by the objective lens at the focus of the eye piece.
`m = ( h )/( f_(e )) xx ( f_(0))/( h ) `
`= ( f_(0))/( f_(e ))`
(b) Given
` f_(0) + f_(e ) = 105, f_(0) = 20 f_(e )`
`20 f_(e ) + f_(e ) = 105 `
`f_(e ) = (105)/( 21) = 5 cm` `:.` Magnification, `m = ( f_(0))/( f_(e )) = ( 100)/( 5) = 20`