Ncert Exercises & Solutions

10.10 Estimate the distance for which ray optics is a good approximation for an aperture of 4 mm and wavelength 400 nm.

Hint: Fresnel’s distance (

Z_{F}

) is the distance that is used in ray optics for a good approximation.

Step 1: Find Fresnel’s distance ( $Z_{F}$ ).

$Z_{F} = \frac{a^{2}}{λ}$
Where,
Aperture width, a = 4 mm = 4 × 10^-3 m
Wavelength of light, $λ$ = 400 nm = 400 × 10^-9 m

$Z_{F} = \frac{{(4 \times 10^{- 3})}^{2}}{400 \times 10^{- 9}} = 40 m$

Therefore, 40 m is the distance for which the ray optics is a good approximation.