Answered

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

Verified Answer :

skyluke89

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.

The wavelength of the light in lucite is \(3.93\times 10^{-7}\) m.

Option 2 is the correct answer.

How do you calculate the wavelength?

Given that monochromatic light (f =5.09 ×1014 Hz) has a wavelength of 589 nanometers in air. We need to calculate the wavelength of light in lucite.

The wavelength can be given as below.

\(\lambda = \dfrac {v}{f}\)

Where v is the speed of light in lucite and f is the frequency of light.

The speed of light in lucite can be calculated as given below.

\(v = \dfrac {c}{n}\)

Where c is the speed of light in air and n is the refractive index of lucite. The accepted value for the refractive index of lucite is 1.50. The speed of light is,

\(v = \dfrac {3\times 10^8}{1.50}\)

\(v = 2 \times 10^8 \;\rm m/s\)

Now the wavelength of light in lucite is,

\(\lambda = \dfrac {2\times 10^8}{5.9 \times 10^{14}}\)

\(\lambda = 3.93 \times 10^{-7} \;\rm m\)

Hence we can conclude that the wavelength of the light in lucite is \(3.93\times 10^{-7}\) m. Option 2 is correct answer.

To know more about the wavelength, follow the link given below.

https://brainly.com/question/7143261.

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