Resolving Power — Prelims Questions

A telescope has an objective lens of diameter $2\,\text{m}$. If it is used to observe light of wavelength $5000,\mathring{A}$, what is its theoretical limit of angular resolution?

To increase the resolving power of a microscope, which of the following changes would be most effective?

Two stars are just resolved by a telescope with an objective lens of diameter $0.5\,\text{m}$ using light of wavelength $600\,\text{nm}$. If another telescope with an objective lens of diameter $1\,\text{m}$ is used, what wavelength of light would be required to achieve the same angular resolution?

Which of the following statements about resolving power is INCORRECT?

An oil immersion objective lens for a microscope has a numerical aperture (NA) of $1.3$. If it uses light of wavelength $450\,\text{nm}$, what is the minimum resolvable distance ($d_{min}$)?

A telescope has an angular resolution of $2 \times 10^{-6},\text{radians}$ for light of wavelength $500\,\text{nm}$. What is the diameter of its objective lens?