It is desired to make an achromatic combination of two lenses, `(L_(1)& L_(2))` made of materials having dispersive power `omega_(1)` and `omega_(2)(ltomega_(1))`. If the combination of lenses is converging then:

Options

A. `L_(1)` is converging
B. `L_(2)` is converging
C. Magnitude power of `L_(1)` is greater than the magnitude power of `L_(2)`
D. both lenses should be conversing.

Answer

B

Explanation

For an achromatic combination of lenses.
`(omega_(1))/(f_(1))+(omega_(2))/(f_(2))=0implies(omega_(1))/(f_(1))=(-omega_(2))/(f_(2))` and `(1)/(f_(eq))=(1)/(f_(1))+(1)/(f_(2))`
power of lens `=(1)/("focal length")` Hence `p_(1)=(1)/(f_(1))` & `p_(2)=(1)/(f_(2))`
So `omega_(1)p_(1)+omega_(2)p_(2)=0`
and `p_(1)+p_(2)gt0`
Now `omega_(2)ltomega_(1)implies(omega_(2))/(omega_(1))lt1implies|(omega_(2))/(omega_(1))|` so `|p_(1)|lt|p_(2)|`
Power of `L_(1)` is less then `L_(2)`
Hence `p_(2)=+ve` and `p_(1)=-ve`