Answer the following questions about a Blu-ray laser: (a) The laser on a Blu-ray player has a wavelength of \(405 \mathrm{nm}\). In what region of the electromagnetic spectrum is this radiation? What is its frequency? (b) A Blu-ray laser has a power of 5 milliwatts ( 1 watt \(=1\ \mathrm{J}\ \mathrm{s}^{-1}\) ). How many photons of light are produced by the laser in 1 hour? (c) The ideal resolution of a player using a laser (such as a Blu-ray player), which determines how close together data can be stored on a compact disk, is determined using the following formula: Resolution \(=0.60(\lambda \text { NA), where } \lambda\) is the wavelength of the laser and NA is the numerical aperture. Numerical aperture is a measure of the size of the spot of light on the disk; the larger the NA, the smaller the spot. In a typical Blu-ray system, NA = 0.95. If the 405-nm laser is used in a Blu-ray player, what is the closest that information can be stored on a Blu-ray disk? (d) The data density of a Blu-ray disk using a 405 -nm laser is \(1.5 \times 10^{7}\) bits \(\mathrm{mm}^{-2}\). Disks have an outside diameter of \(120 \mathrm{mm}\) and a hole of \(15-\mathrm{mm}\) diameter. How many data bits can be contained on the disk? If a Blu-ray disk can hold 9,400,000 pages of text, how many data bits are needed for a typed page? (Hint: Determine the area of the disk that is available to hold data. The area inside a circle is given by \(\mathrm{A}=\pi r^{2},\) where the radius \(r\) is one-half of the diameter.)

Step by step solution

01

Determine the Region of Electromagnetic Spectrum

The wavelength given for the Blu-ray laser is 405 nm. This falls into the visible light spectrum, specifically at the edge of the visible spectrum transitioning into the ultraviolet range.

02

Calculate the Frequency of the Laser

To find the frequency (f) of the laser, use the equation for the speed of light (c), where c = wavelength (lambda) * frequency (f). The speed of light c is approximately \(3 \times 10^8 \text{m/s}\). Convert the wavelength from nanometers to meters by dividing by \(10^9\), and then use the formula \(f = \frac{c}{\lambda}\) to find the frequency.

03

Calculate Number of Photons Produced in 1 Hour

Using the power of the Blu-ray laser (5 milliwatts), convert it to watts by dividing by 1000. Then calculate the energy per photon using the formula \(E = hf\), where h is Planck's constant (\(6.626 \times 10^{-34} \text{J s}\)). Divide the laser power by the energy per photon to find the number of photons emitted per second. To find the number of photons emitted in 1 hour, multiply by the number of seconds in an hour (3600).

04

Calculate the Resolution of the Blu-ray Player

Substitute the wavelength (405 nm) and the numerical aperture (NA = 0.95) into the resolution formula \(\text{Resolution} = 0.60(\lambda \text{ NA})\) and solve for the resolution.

05

Determine the Area of the Disk Available for Data

First, calculate the radius of the outer disk and the radius of the hole by taking one-half of their respective diameters. Then find the area of each circle using \(A = \pi r^{2}\). Subtract the area of the hole from the area of the entire disk to get the data-storing area of the disk.

06

Calculate the Total Number of Bits on the Disk

Multiply the data density (\(1.5 \times 10^{7} \text{bits/mm}^{2}\)) by the data-storing area of the disk to find the total number of data bits contained on the disk.

07

Determine the Number of Data Bits Per Typed Page

Divide the total number of data bits on the disk by the number of pages of text the disk can hold (9,400,000) to find the number of bits needed for one typed page.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding the Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, which differ in wavelength and frequency. The Blu-ray laser utilized in our textbook exercise operates at a 405 nm wavelength, placing it at the very boundary between the visible light range and the ultraviolet region. The visible light spectrum, familiar to us all, spans from about 380 nm to 750 nm.

Understanding how the Blu-ray operates within the electromagnetic spectrum is crucial because its position determines its behavior, including its frequency. Frequency is inversely proportional to the wavelength, meaning that as the wavelength of light decreases, its frequency increases. This high frequency allows for the encoding of data at a higher resolution, which is central to the Blu-ray technology's advantages.

Photon Emission and Blu-ray Laser Power

Photon emission is a fundamental concept in understanding how lasers work. Blu-ray lasers emit photons when they are powered on, and these photons carry the data that is recorded on the disc. In the exercise, we calculate the number of photons a Blu-ray laser emits in an hour based on its power, which is 5 milliwatts.

This calculation involves understanding the concept of energy per photon, which is given by the equation using Planck's constant. By dividing the laser's power by the energy per photon, we can determine the emission rate of photons. High photon emission rates are crucial for achieving the data transfer speeds necessary for Blu-ray players to function effectively.

Data Storage Resolution on Blu-ray Discs

One of the most significant features of Blu-ray technology is its resolution—how closely data can be stored on a disc. This is governed by the formula provided in our textbook exercise, incorporating the wavelength of the laser and the numerical aperture. The numerical aperture (NA) is a critical factor in the design of optical systems and corresponds to the size of the light spot on the disc.

A larger NA results in a smaller spot, allowing data to be packed more densely. The high resolution of Blu-ray discs, as derived from the formula, directly determines the data storage capacity, making it possible to store large volumes of high-definition content on a compact disc.