A microscope has an objective lens with an aperture of diameter 0.50 cm where a monochromatic light source of wavelength 580 nm is used to illuminate the object.It is determined that the minimum angle of resolution is 1.15 x 10^-4 rad.If the illuminating source were replaced by an violet source of wavelength 420 nm,what would the minimum angle of resolution now become? (1 nm = 10^-9m) A)1.7 x 10^-4 rad B)1.0 x 10^-4 rad C)0.83 x 10^-4 rad D)0.50 x 10^-4 rad

Question

Quizplus · Accepted Answer

The minimum angle of resolution is given by the Rayleigh criterion: 
θ = 1.22 λ / D 
where λ is the wavelength of light, D is the diameter of the aperture, and θ is the minimum angle of resolution. 
For the given microscope with a monochromatic light source of wavelength 580 nm, we have: 
θ = 1.22 (580 nm) / (0.50 cm) = 1.41 x 10^-4 rad 
For a violet source of wavelength 420 nm, we have: 
θ' = 1.22 (420 nm) / (0.50 cm) = 1.12 x 10^-4 rad 
Therefore, the minimum angle of resolution with the violet source is smaller than with the monochromatic source, which makes sense since shorter wavelengths of light allow for higher resolution. The closest answer choice to 1.12 x 10^-4 rad is C, 0.83 x 10^-4 rad.

A Microscope Has an Objective Lens with an Aperture of Diameter