/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 39 When light strikes the surface b... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

When light strikes the surface between two materials from above, the Brewster angle is \(65.0^{\circ} .\) What is the Brewster angle when the light encounters the same surface from below?

Short Answer

Expert verified
The Brewster angle from below is also \(65.0^{\circ}\).

Step by step solution

01

Understand Brewster's Angle

Brewster's angle, also known as the polarization angle, occurs when the light reflected off a surface is completely polarized. This happens when the angle of incidence is such that the refracted and reflected rays are perpendicular to each other.
02

Identify the Known Brewster's Angle

The problem states that the Brewster angle is \(65.0^{\circ}\) when light encounters the surface from above. This means that, for the two materials involved, this angle results in the polarization condition described in Step 1.
03

Apply Reciprocity Principle

The Brewster angle depends only on the indices of refraction of the two materials, not on the direction of the light. According to the principle of reciprocity, the Brewster angle from below will be the same as from above if the indices of refraction remain unchanged.
04

Conclusion

Since the Brewster angle only depends on the indices of refraction, and these indices do not change with the direction of light, the Brewster angle for the light encountering the surface from below is the same as from above, which is \(65.0^{\circ}\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

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

Polarization
Polarization refers to the orientation of the oscillations of electromagnetic waves, such as light. Normally, light vibrates in multiple planes. However, when light is polarized, its waves oscillate primarily in one direction. One way to achieve polarization is through reflection. When light is reflected at a specific angle, known as the Brewster's angle, it becomes fully polarized.

This is particularly important when considering light's interactions with different surfaces. At Brewster's angle, the reflected light is polarized parallel to the surface. This occurs because the angle of incidence is such that the reflected and refracted rays are perpendicular to each other. Therefore, understanding polarization is crucial in fields like photography and optics to reduce glare and improve clarity.
Angle of Incidence
The angle of incidence is the angle between the incoming light ray and the perpendicular (normal) to the surface at the point of contact. This angle plays a vital role in determining how light behaves upon hitting a surface. In the case of Brewster's angle, the angle of incidence is uniquely significant.

At Brewster's angle, the light's reflection is minimized while its transmission is maximized through the surface. This specific angle is crucial because it leads to polarization of the reflected ray. By understanding and calculating the correct angle of incidence, engineers and scientists can manipulate light for various applications, such as reducing reflections or achieving specific optical effects. This knowledge is used in designing lenses and other optical devices.
Refracted and Reflected Rays
When light encounters a boundary between two materials, it splits into two rays: the refracted ray, which passes into the other medium, and the reflected ray, which bounces back into the original medium. The behavior of these rays depends on the angle of incidence and the properties of the materials involved.

At Brewster's angle, something unique happens. The angle of incidence results in the reflected and refracted rays being perpendicular to each other. This specific configuration leads to complete polarization of the reflected light. The relationship between these rays is essential for understanding phenomena involving light, such as glare and rainbow formation.
  • The refracted ray bends according to Snell's Law, which relates the angle of incidence to the angle of refraction through the indices of refraction of the two media.
  • The reflected ray follows the law of reflection, which states that the angle of incidence is equal to the angle of reflection.
This interplay is foundational to optical engineering and helps in designing devices like polarizers and anti-glare coatings.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The drawing shows a ray of light traveling through three materials whose surfaces are parallel to each other. The refracted rays (but not the reflected rays) are shown as the light passes through each material. A ray of light strikes the \(a-b\) interface at a \(50.0^{\circ}\) angle of incidence. The index of refraction of material \(a\) is \(n_{a}=1.20 .\) The angles of refraction in materials \(b\) and \(c\) are, respectively, \(45.0^{\circ}\) and \(56.7^{\circ} .\) Find the indices of refraction in these two media.

A spectator, seated in the left-field stands, is watching a baseball player who is \(1.9 \mathrm{m}\) tall and is \(75 \mathrm{m}\) away. On a \(\mathrm{TV}\) screen, located \(3.0 \mathrm{m}\) from a person watching the game at home, the image of this same player is \(0.12 \mathrm{m}\) tall. Find the angular size of the player as seen by (a) the spectator watching the game live and (b) the TV viewer. (c) To whom does the player appear to be larger?

A converging lens \((f=12.0 \mathrm{cm})\) is located \(30.0 \mathrm{cm}\) to the left of a diverging lens \((f=-6.00 \mathrm{cm}) .\) A postage stamp is placed \(36.0 \mathrm{cm}\) to the left of the converging lens. (a) Locate the final image of the stamp relative to the diverging lens. (b) Find the overall magnification. (c) Is the final image real or virtual? With respect to the original object, is the final image (d) upright or inverted, and is it (e) larger or smaller?

The lengths of three telescopes are \(L_{\mathrm{A}}=455 \mathrm{mm}, L_{\mathrm{B}}=615 \mathrm{mm},\) and \(L_{C}=824 \mathrm{mm} .\) The focal length of the eyepiece for each telescope is 3.00 mm. Find the angular magnification of each telescope.

To focus a camera on objects at different distances, the converging lens is moved toward or away from the image sensor, so a sharp image always falls on the sensor. A camera with a telephoto lens \((f=200.0 \mathrm{mm})\) is to be focused on an object located first at a distance of \(3.5 \mathrm{m}\) and then at \(50.0 \mathrm{m} .\) Over what distance must the lens be movable?

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.