Question

Diffraction spreading for a flashlight is insignificant compared with other limitations in its optics, such as spherical aberrations in its mirror. To show this, calculate the minimum angular spreading in rad of a flashlight beam that is originally 5.90 cm in diameter with an average wavelength of 610 nm.

Answer 1

Answer:

The answer is "$1.2566 \times 10^{-5}\,rad$".

Explanation:

As per the Rayleigh Criterion the minimum angular spreading, for a circular aperture:

$\theta_{\mathrm{min}}\approx \sin\theta=1.22\,\frac{\lambda}{d}$  

$\theta_{\mathrm{min}}=\mathrm{1.22\,\frac{\left( 610\,nm \right)}{\left( 5.90\,cm \right)}=1.22\,\frac{\left( 610\times10^{-9}\,m \right)}{\left( 5.90\times10^{-2}\,m \right)}}$

                               $=1.22\times 103.389 \times 10^{-7}\\\\=1.22\times 1.03 \times 10^{-5}\\\\=\mathrm{1.2566 \times 10^{-5}\,rad}$