Two lenses have focal lengths f1 f2 and their dispersive powers are ω1 ω2 respectively. They will together form an achromatic combination if:

Question

Two lenses have focal lengths f1 f2 and their dispersive powers are ω1 ω2 respectively. They will together form an achromatic combination if: (A) ω1 f1=w2 f2 (B) ω1 f 2+ω2 f 1=0 (C) ω1+f1=ω1 f2 (D) ω1-f1=ω2-f2

Tardigrade Admin · Accepted Answer

For achromatic combination (ω1/f1)+(ω2/f2)=0 ∴ ω1 f2+ω2 f1=0

Q. Two lenses have focal lengths $f_{1} & f_{2}$ and their dispersive powers are $ω_{1} & ω_{2}$ respectively. They will together form an achromatic combination if:

$ω_{1} f_{1} = w_{2} f_{2}$

$ω_{1} f_{2} + ω_{2} f_{1} = 0$

$ω_{1} + f_{1} = ω_{1} f_{2}$

$ω_{1} - f_{1} = ω_{2} - f_{2}$

For achromatic combination
$\frac{ω _{1}}{f _{1}} + \frac{ω _{2}}{f _{2}} = 0$
$∴ ω_{1} f_{2} + ω_{2} f_{1} = 0$

Q. Two lenses have focal lengths f1​&f2​ and their dispersive powers are ω1​&ω2​ respectively. They will together form an achromatic combination if:

ω1​f1​=w2​f2​

ω1​f2​+ω2​f1​=0

ω1​+f1​=ω1​f2​

ω1​−f1​=ω2​−f2​