Question

Find the range of visible wavelengths of light in crown glass.

Short answer

The visible light wavelengths in crown glass span from \({\rm{250}}\;{\rm{nm}}\) to \({\rm{500}}\;{\rm{nm}}\).

Step-by-step solution

Define wavelength

The wavelength of a wave is defined as the distance between two identical locations in a wave pattern.

Explanation

The speed of an electromagnetic wave can be defined by the formula,

\(\frac{{\rm{c}}}{\lambda } = \nu \)

Where \(\nu \) and \(\lambda \) are the frequency and wavelength of the light, respectively.

The visible light has wavelengths ranging from \({\rm{380}}\;{\rm{nm}}\) to \({\rm{760}}\;{\rm{nm}}\).

The wavelength of an electromagnetic wave in a medium can be given as,

\({\lambda _{\rm{n}}} = \frac{\lambda }{{\rm{n}}}\)

where \(\lambda \) is the wavelength of the electromagnetic wave in a vacuum and \({\rm{n}}\)is the refraction index of the specified medium.

Light travels from the air to the water. The crown glass has a refractive index of

\({{\rm{n}}_{{\rm{CG}}}} = {\rm{1}}{\rm{.52}}\)

Evaluating the range of visible wavelengths of light

Calculate the lower bound for the wavelengths of light waves (for the violet light):

The bottom bound of the light wave wavelength in the vacuum is \({\rm{380}}\;{\rm{nm}}\). The wavelength of an electromagnetic wave in a medium is determined by,

\(\begin{array}{c}{\lambda _{\rm{n}}} = \frac{{{\lambda _{{\rm{violet}}}}}}{{{{\rm{n}}_{{\rm{CG}}}}}}\\\; = \frac{{{\rm{380}}\;{\rm{nm}}}}{{{\rm{1}}{\rm{.52}}}}\\ = {\rm{250}}\;{\rm{nm}}\end{array}\)

Now, calculate the upper bound of the wavelengths of light waves (for the red light):

The red bound of the light wave wavelength in the vacuum is \({\rm{760}}\;{\rm{nm}}\).The wavelength of an electromagnetic wave in a medium is determined by,

\(\begin{array}{c}{\lambda _{\rm{n}}} = \frac{{{\lambda _{{\rm{red}}}}}}{{{{\rm{n}}_{{\rm{CG}}}}}}\\ = \frac{{{\rm{760}}\;{\rm{nm}}}}{{{\rm{1}}{\rm{.52}}}}\\\; = {\rm{500}}\;{\rm{nm}}\end{array}\)

As a result, visible light wavelengths in crown glass span from \({\rm{250}}\;{\rm{nm}}\) to \({\rm{500 nm}}\)