Estimate the distance for which ray optics is good approximationfor an aperture of 4 mm and wavelength 400 nm.
The distance for which the ray optics is a good approximation is known as the Fresnel’s distance.
Fresnel’s distance is given by,
Z F = a 2 λ
Where, Z F is the Fresnel’s distance, a is the aperture width and λ is the wavelength.
Aperture width is given as 4 mm = 4 × 10 − 3 m .
Wavelength of the light is given as λ = 400 nm = 100 × 10 − 9 m .
Substitute the values in the above formula.
Z F = ( 400 × 10 − 3 ) 2 400 × 10 − 9 = 40 m
Thus, the distance for which the ray optics is a good approximation is 40 m .
The distance for which the ray optics is a good approximation is known as the Fresnel’s distance.
Fresnel’s distance is given by,
Where,
Aperture width is given as
Wavelength of the light is given as
Substitute the values in the above formula.
Thus, the distance for which the ray optics is a good approximation is
