Question

A helium-neon laser beam has a wavelength in air of 633 nm. It takes 1.38 ns for the light to travel through 32.0 cm of an unknown liquid. What is the wavelength of the laser beam in the liquid?

Answer 1

Answer:

Wavelength = 489.52 nm

Explanation:

Given that the wavelength of the light = 633 nm

The time taken by the light in unknown liquid = 1.38 ns

Also,

1 ns = 10⁻⁹ s

So, t = 1.38 × 10⁻⁹ s

Also,

Distance = 32.0 cm = 0.32 m ( 1 cm = 0.01 m)

So, speed of the light in the liquid = Distance / Time = 0.32 / 1.38 × 10⁻⁹ m/s = 2.32 × 10⁸  m/s

Frequency of the light does not change when light travels from one medium to another. So,

$\frac {V_{air}}{\lambda_{air}}=\frac {V_{liquid}}{\lambda_{liquid}}$

${V_{air}}=3\times 10^8\ m/s$

${\lambda_{air}}=633\ nm$

${V_{liquid}}=2.32\times 10^8\ m/s$

${\lambda_{liquid}}=?\ nm$

So,

$\frac {3\times 10^8\ m/s}{633\ nm}=\frac {2.32\times 10^8\ m/s}{\lambda_{liquid}}$

Wavelength = 489.52 nm