Question

A microscope using ultraviolet light is used to study bacteria. If the aperture diameter is 1.5 cm and it is desired to distinguish features with an angular size 0.036 arc seconds, what maximum wavelength can be used

Answer 1

Given :

A microscope using ultraviolet light is used to study bacteria. If the aperture diameter is 1.5 cm.

Angular size is 0.036 arc seconds.

To Find :

The maximum wavelength that can be used.

Solution :

Converting given angle into radians :

$\theta = \dfrac{0.036}{3600}\times \dfrac{\pi}{180}\\\\\theta = 1.745\times 10^{-7}\ radians$

Now, we know maximum wavelength is given by :

$\lambda = \dfrac{\theta \times D}{1.22}\\\\\lambda = \dfrac{1.745\times 10^{-7} \times 0.015}{1.22}\ m\\\\\lambda =2.145 \times 10^{-7}\ m$

Hence, this is the required solution.