For what distance ray optics is a good approximation when the aperture is 4 mm and the wavelength of light is 400 nm ?

Question

For what distance ray optics is a good approximation when the aperture is 4 mm and the wavelength of light is 400 nm ? (A) 24 m (B) 40 m (C) 18 m (D) 30 m

Tardigrade Admin · Accepted Answer

Rays optics is good approximation up to a distance equal to Fresnel's distance

(I_{F})

.
From the formula of Fresnel's distance,

D_{f} = \frac{a ^{2}}{λ}

Here,

a = 4 mm = 4 \times 1 0^{- 3} m

λ = 400 nm = 400 \times 1 0^{- 9} m

D_{f} = \frac{( 4 \times 1 0 ^{- 3} ) ^{2}}{4 \times 1 0 ^{- 7}}

= \frac{4 \times 4 \times 1 0 ^{- 3} \times 1 0 ^{- 3}}{4 \times 1 0 ^{- 7}} = 40 m

Q. For what distance ray optics is a good approximation when the aperture is $4 mm$ and the wavelength of light is $400 nm$ ?

$24 m$

$40 m$

$18 m$

$30 m$

Q. For what distance ray optics is a good approximation when the aperture is 4mm and the wavelength of light is 400nm ?

24m

40m

18m

30m

Rays optics is good approximation up to a distance equal to Fresnel's distance (IF​) . From the formula of Fresnel's distance, Df​=λa2​ Here, a=4mm=4×10−3m λ=400nm=400×10−9m Df​=4×10−7(4×10−3)2​ =4×10−74×4×10−3×10−3​=40m

Q. For what distance ray optics is a good approximation when the aperture is $4 mm$ and the wavelength of light is $400 nm$ ?

$24 m$

$40 m$

$18 m$

$30 m$