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

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

Step-by-step 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 * 10^(-9) \text{ m} = 7*10^(-7) \text{ m}`

Diameter of grain of sand =
`0.2 * \text{ mm} = 0.2*10^(-3)\text{ m} = 2*10^(-4)\text{ m}`

It is seen that the grain of sand is larger.

The ratio of the sizes is given by

`\frac{2*10^(-4) \text{ m}}{7*10^(-7) \text{ m}}=286`