Question

The resolving power of a compound microscope will increase with
(a)The decrease in wavelength of light and an increase in numerical aperture
(b)Increase in wavelength of light and decrease in numerical aperture
(c)Increase in both wavelength of light and numerical aperture
(d)The decrease in both wavelength of light and numerical aperture

Answer 1

Hint: It is directly proportional to the refractive index of the medium and indirectly proportional to the wavelength while independent of the focal length of the lens.

Complete answer:
The resolving power of the microscope increases with the decrease in wavelength of light and an increase in the numerical aperture. Resolving power of the compound microscope is the ability of the compound microscope to form a separate image of two close objects which are placed very near to each other. This is given by the famous Abbe's criterion given by Ernst Abbe in 1873.
-Resolving power can be measured by,
$ResolvingPower={\displaystyle \frac{0.61\lambda }{NA}}$
-The minimum distance between two objects can be explained as-
 $d_{min}={\displaystyle \frac{1.22\lambda }{2nsin\theta }}$
or, $d_{min}={\displaystyle \frac{0.61\lambda }{nsin\theta }}$
-And the resolving power is inversely proportional to the minimum distance between the objects so,
$Resolvingpower={\displaystyle \frac{1}{d_{min}}}$
$Resolvingpower={\displaystyle \frac{nsin\theta }{0.61\lambda }}$
Where lambda is the wavelength of light and $nsin\theta$ is the numerical aperture.
It can be observed from the formula that the resolving power is directly proportional to the numerical aperture but is indirectly proportional to the wavelength of the light.
So, the correct answer is a ‘Decrease in wavelength of the light used and an increase in the numerical aperture’.

Note:
-The compound microscope gives higher magnification because it uses two sets of lenses.
-The resolving power of the compound microscope remains unchanged when the focal length of the lens increases.