Question

A beam of monochromatic light (f =5.09 ×1014 Hz) has a wavelength of 589 nanometers in air. What is the wavelength of this light in Lucite?
(1)150 nm
(2)393 nm
(3)589 nm
(4)884 nm

Answer 1

Lucite has a refractive index of n=1.50. This means that the speed of the light in lucite is decreased according to:
$v=\frac{c}{n}$
where $c=3 \cdot 10^8 m/s$ is the speed of light in air. Putting the number in the formula, we find that the speed of light in lucite is
$v=\frac{3 \cdot 10^8 m/s}{1.50}=2\cdot 10^8 m/s$
The frequency of the light is $f=5.09 \cdot 10^{14}Hz$, so now we can calculate the wavelength in lucite by using the formula:
$\lambda=\frac{v}{f}=\frac{2\cdot 10^8 m/s}{5.09 \cdot 10^{14} Hz}=3.93 \cdot 10^{-7} m=393 nm$
Therefore, the correct answer is (2) 393 nm.