Question

5. A microscope has an objective of aperture
8mm and focal length of 5cm. The minimum
separation between two objects to be just
resolved by the microscope is (wavelength
of light used 5 000 Å )
[TS-EAMCET-22.04.18]
1) 2.2 um 2) 3.4 um 3) 4.23 um 4) 3.6 um​

Answer 1

A microscope has an objective of aperture 8 mm and focal length of 5mm. wavelength of light, λ = 5500 A°

The minimum seperation between two objects to be just resolved by the microscope is ...

solution : The minimum seperation between two objects to be just resolved by the microscope is given by, $d_{min}=\frac{1.22\lambda f}{D}$

where f is focal length of objective lens , D is diameter of objective lens.

here λ = 5500 A° = 5.5 × 10^-7 m

f = 5cm = 5 × 10¯² m

D = 8 mm = 8 × 10¯³ m

now $d_{min}$ = (1.22 × 5.5 × 10^-7 × 5 × 10¯²)/(8 × 10¯³)

= (1.22 × 5.5 × 5)/(8) × 10¯⁶ m

= 4.19 × 10¯⁶ m ≈ 4.2 μm

Therefore the minimum seperation between two objects to be just resolved by the microscope is 4.2 μm