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 5.85 cm in diameter with an average wavelength of 580 nm

Answer 1

Answer:

 $\theta_{min} = 1.21 \times 10^{-5}\ rad$

Explanation:

given,

diameter of the beam (d)= 5.85 cm

                                        = 0.0585 m

average wavelength of the(λ) = 580 n m

angle of of spreading = ?

according to the Rayleigh Criterion the minimum angular spreading, for a circular aperture, is

                $\theta_{min} = 1.22\ \dfrac{\lambda}{d}$

                $\theta_{min} = 1.22\ \dfrac{580 \times 10^{-9}}{0.0585}$

                $\theta_{min} = 1.22\times 9.145 \times 10^{-6}$

               $\theta_{min} = 1.21 \times 10^{-5}\ rad$

the minimum angle of spreading is $\theta_{min} = 1.21 \times 10^{-5}\ rad$