Question

A microscope has an objective of aperture 8mm and focal length of 5cm the minimum separation between two objects to be just resolved by microscope wavelength 5500

Answer 1

it has given that, A microscope has an objective of aperture 8mm and focal length of 5 cm.

we have to find the minimum seperation between two objects to be just resolved by microscope wavelength 5500 A° .

solution : The minimum seperation between two objects to be just resolved by microscope is given by, d = 1.22λf/NA

where NA is numerical aperture of objective lens, f is Focal length of lens and λ is wavelength.

here , λ = 5500 A° = 5.5 × 10^-7 m

f = 5cm = 5 × 10^-2 m

NA = 8 mm = 8 × 10^-3 m

now, d = (1.22 × 5.5 × 10^-7 × 5 × 10^-2)/(8 × 10^-3)

= (1.22 × 5.5 × 5)/8 × 10^-6

= 4.193 × 10¯⁶ m ≈ 4.2 μm

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