# Explain giving reason, how the resolving power of a compound microscope depends on the (a) frequency of the incident light. (b) focal length of the objective lens.

The resolving power of the compound microscope is given as :

$=\frac{2u\sin \theta }{1.22\lambda }$

and     $\lambda = c/v$

there, resolving power $=\frac{2u\sin \theta\times v }{1.22\; c }$

(a) According to the formula,

$R.P=\frac{2\times u\times \sin \theta \times v}{1.22\times c}$

Since the frequency of the incident light will increase as the resolving power (R.P) is directly proportional to the frequency of light.

(b) Resolving power of the compound microscope is not independent of the focal length of the objective lens, instead, it varies inversely with the focal length of the objective lens,

as per the formula; $d_{min}=\frac{1.22f\lambda }{D}$

Since,

Resolving power $=\frac{1}{d_{min}}=\frac{1}{\frac{1.22f\lambda }{D}}=\frac{D}{1.22f\lambda }$

Hence,

Resolving power is inversely proportional to the focal length.

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