MCQ
The ratio of resolving powers of an optical microscope for two wavelengths $\lambda_1 = 4000\,\mathring A$ and $\lambda_2 = 6000 \,\mathring A$ is
- A$9:4$
- ✓$3:2$
- C$16$$:81$
- D$\;8:27$
✓
Answer
Correct option: B.
$3:2$
b
The resolving power of an optical microscope,
The resolving power of an optical microscope,
$\mathrm{RP}=\frac{2 \mu \sin \theta}{\lambda}$
For wavelength ${\lambda _1} = 4000\,\mathop {\text{A}}\limits^o $, resolving power will be
$\mathrm{RP}_{1}=\frac{2 \mu \sin \theta}{4000}$ ..... $(i)$
For wavelength ${\lambda _2} = 6000\,\mathop {\text{A}}\limits^o $, resolving power will be
$\mathrm{RP}_{2}=\frac{2 \mu \sin \theta}{6000}$ ..... $(ii)$
On dividing eqn. $(i)$ by eqn. $(ii)$
$=\frac{\mathrm{RP}_{1}}{\mathrm{RP}_{2}}=\frac{6000}{4000}=\frac{3}{2}$
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