Question

The wavelength of red light is about 700 nm: λred = 700 nm. Which is larger, a grain of sand (diameter roughly 0.2 mm) or a wave of red light? How many times larger?

Answer 1

Answer:

The grain of sand is larger by a factor of about 286.

Explanation:

We express both values in standard form in the SI unit of metre so that the comparison can be easily done:

$\lambda_R = 700 \text{ nm} = 700 \times 10^{-9} \text{ m} = 7\times10^{-7} \text{ m}$

Diameter of grain of sand = $0.2 \times \text{ mm} = 0.2\times10^{-3}\text{ m} = 2\times10^{-4}\text{ m}$

It is seen that the grain of sand is larger.

The ratio of the sizes is given by

$\dfrac{2\times10^{-4} \text{ m}}{7\times10^{-7} \text{ m}}=286$