First slide

Diffraction

Question

The ratio of resolving powers of an optical microscope for two wavelengths $λ_{1} = 4000 \overset{0}{A}$ and $λ_{2} = 6000 \ AA is$

Easy

A

9 : 4
B

3 : 2
C

16 : 81
D

8 : 27

Solution

The resolving power of an optical microscope,
$RP = \frac{2 μ \sin θ}{λ}$
$For wavelength λ_{1} = 4000 \overset{0}{A}, resolving power will be$
${RP}_{1} = \frac{2 μ \sin θ}{4000} . . . . (i)$
$For wavelength λ_{2} = 6000 \overset{0}{A,} resolving power will be$
${RP}_{2} = \frac{2 μ \sin θ}{6000} . . . . (i i)$
On dividing eqn. (i) by eqn. (ii)
$\frac{{RP}_{1}}{{RP}_{2}} = \frac{6000}{4000} = \frac{3}{2}$

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