Two lenses in contact made of materials with dispersive powers in the ratio `2:1` , behaves as an achromatic diverging lens of focal length 10 cm . The individual focal length of the lenses are:

Options

A. 5 cm, -10 cm
B. -5 cm, 10 cm
C. 10 cm, -20 cm
D. -20 cm, 10 cm

Answer

A

Explanation

For the achromatic combination of lens ` ( omega _ 1 ) /( f _ 1 ) + ( omega _ 2 ) / ( f _ 2 ) = 0 ` ….. ( 1 ) where , ` omeg _ 1 and omega _ 2 ` are the dispersive powers of the lenses. For the equivalent focal length, ` ( 1 ) /( f _ 1 ) + ( 1 ) /( f _ 2 ) = ( 1 ) / ( f _ e ) `
` rArr ( 1 ) /( f _ 1 ) + ( 1 ) /( f_ 2 ) = ( 1 ) / ( 10) `.... ( 2 ) [ since, ` f _ e = 10 ` cm ]
` (omega _ 1 ) / ( omega _ 2 ) = ( 2 ) / ( 1 ) = - ( f _ 1 ) /( f _ 2 ) ` ... (3 ) (Given in the question )
From equation (1), (2) and (3) we get, ` f _ 2 = 5 ` cm , ` f _ 1 = - 10` cm.