Question

For achromatic combination of lenses, if we use two lenses of focal length and $f$ respectively, dispersive powers $ω$ and $ω,$ then:

• A. $ω={ω}_0,{ω}^{′}=2{ω}_0,f^{′}=2f$
• B. $ω={ω}_0,{ω}^{′}=2{ω}_0,f^{′}=−2f$
• C. $ω={ω}_0,{ω}^{′}=2{ω}_0,f^{′}=f/2$
• D. $ω={ω}_0,{ω}^{′}=2{ω}_0{f}^{′}=−f/2$

Answer 1

Answer: (B)

The condition of achromatic combination is
$\frac{ω}{{ω}^{′}}=−\frac{f}{f^{′}}$
This is satisfied if
$ω={ω}_0,{ω}^{′}=2{ω}_0$ and $f=2f$
So that, $\frac{{ω}_0}{2{ω}_0}=\frac{−f}{−2f}$
$⇒\frac{1}{2}=\frac{1}{2}$