Q144 / 160 · TS EAMCET 2020 (11 Sep Shift 2) · Physics

Wavelength of light used in an optical instruments are $\lambda_1=4000 Å$ and $\lambda_2=5000 Å$, then the ratio of their respective resolving powers (corresponding to $\lambda_1$ and $\lambda_2$ ) is

  • A
    $3: 5$
  • B
    $9: 1$
  • C
    $4: 5$
  • Correct answer
    D
    $5: 4$

Solution

As we know that, Resolving power of optical instrument, $\mathrm{RP}=\frac{2 \mu \sin \theta}{1.22 \lambda} \Rightarrow \mathrm{RP} \text { or } R \propto \frac{1}{\lambda}$ Hence, ratio of resolving power of two instruments is $\frac{R_1}{R_2}=\frac{\lambda_2}{\lambda_1} \Rightarrow \frac{R_1}{R_2}=\frac{5000}{4000}$ $\left[\because \lambda_1=4000 Å\right.$ and $\left.\lambda_2=5000 Å\right]$ $\frac{R_1}{R_2}=\frac{5}{4}$ or $5: 4$

Hence, the correct answer is option: 'D'.

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