Q143 / 160 · AP EAMCET 2018 (22 Apr Shift 2) · Physics

A microscope has an objective of aperture $8 \mathrm{~mm}$ and focal length of $5 \mathrm{~cm}$. The minimum separation between two objects to be just resolved by the microscope is (wavelength of light used $=5500 Å$ )

  • A
    $2.2 \mu \mathrm{m}$
  • B
    $3.4 \mu \mathrm{m}$
  • Correct answer
    C
    $4.2 \mu \mathrm{m}$
  • D
    $3.6 \mu \mathrm{m}$

Solution

Minimum separation for a microscope, so that images of 2-near by objects are just resolved is given by $$ \begin{aligned} d_{\min } & =\frac{1.22 f \lambda}{D}=\frac{1.22 \times 5 \mathrm{~cm} \times 5500 Å}{8 \mathrm{~mm}} \\ & =\frac{1.22 \times 5 \times 10^{-2} \times 5500 \times 10^{-10}}{8 \times 10^{-3}} \\ & =41.9 \times 10^{-7} \mathrm{~m}=4.19 \times 10^{-6} \mathrm{~m}=4.2 \mu \mathrm{m} \end{aligned} $$

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

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