Question

Ray optics is valid when characteristic dimensions are
A. Of the same order as the wavelength of the light.
B. Much smaller than the wavelength of the light.
C. Much larger than the wavelength of the light.
D. Of the order of $1mm$.$$1mm$$

Answer 1

Hint:To solve this question, we need to know the relation between the characteristic dimensions or the size of the object and the wavelength of the light to make the ray optics valid. This can be obtained by the minimum distance a light ray has to travel before it bends from its original path which is known as fresnel distance. Therefore, we will understand the concept of fresnel distance first and then reach our final answer.

Complete answer:
Here, we are asked about the relation between the size of the source and the wavelength of the light for which the ray optics are valid.Validity of Ray optics can be explained by the help of the fresnel distance. It can be defined as the minimum distance that a light ray has to travel before it bends from its original path.

Mathematically, we can write the formula of fresnel distance as:
$$Z_f={\displaystyle \frac{d^2}{\lambda }}$$
where $Z_f$ is the Fresnel distance, $d$ is the size of the source and $\lambda$ is the wavelength of the light used.As the light ray must travel at least this distance to bend from its original path, we can say by the formula that the size of the source should be much larger than the wavelength of the light to apply the ray optics.Thus, it can be concluded that Ray optics is valid when characteristic dimensions are much larger than the wavelength of the light.

Hence, option C is the right answer.

Note:We have seen the concept of Fresnel distance in this question. We can say that this is the distinguishing boundary between ray optics and wave optics. In other words, if the wavelength is comparable to the size of the source or the object, then diffraction could happen, however it cannot be explained using ray optics. For this, we need to use the concept of wave optics.