A lady uses $+1.5D$ glasses to have normal vision from $25cm$ onwards. She uses a $20D$ lens as a simple microscope to see an object. The maximum magnifying powers if she uses the microscope (a) together with the glasses and (b) without the glasses are

The correct option is B 6, 9
Convex lenses (with positive power) are used to correct hypermetropia (far-sightedness). Hence, we can estimate that the lady's near point is greater than the normal value ($25cm$).

Focal length of the correctional lens
$f=\frac{1}{P}=\frac{1}{1.5D}=\frac{10\times 100}{15}cm=\frac{200}{3}cm$

Power of the magnifier lens $P_m=20D$

Focal length of the magnifier $f_m=\frac{100}{20}=5cm$

Maximum magnification is given by

$m=1+\frac{D}{f_m}$

Case (a) with correctional glasses

The eye with correctional glasses will behave as a normal eye. Hence $D=25cm$
$m=1+\frac{25}{5}=6$

Case (b) without correctional glasses


For an object at the normal near point ($25cm$), the lens in the correctional glasses will form an image at her actual near point. Let the actual near point be $vcm$

Then using lens formula,
$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$
$u=D=25cm$, $f=\frac{200}{3}cm$
$\Rightarrow v=-40cm$.

So the actual near point is at $40cm$.

Then magnification without correctional glasses $m=1+\frac{40}{f_o}=1+\frac{40}{5}=1+8=9$