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

`\theta_(min) = 1.21 * 10^(-5)\ rad`

Step-by-step 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\ (\lambda)/(d)`

`\theta_(min) = 1.22\ (580 * 10^(-9))/(0.0585)`

`\theta_(min) = 1.22* 9.145 * 10^(-6)`

`\theta_(min) = 1.21 * 10^(-5)\ rad`

the minimum angle of spreading is
`\theta_(min) = 1.21 * 10^(-5)\ rad`