Question

In: Physics

The angle of incidence of a light beam in air onto a reflecting surface is continuously...

The angle of incidence of a light beam in air onto a reflecting surface is continuously variable. The reflected ray is found to be completely polarized when the angle of incidence is 48.0. (a) What is the index of refraction of the reflecting material? (b) If some of the incident light (at an angle of 48.0) passes into the material below the surface, what is the angle of refraction?

Solutions

Expert Solution

Concepts and reason

The required concept to solve the problem is Brewster's law and polarization. First, using Brewster's law, find the refractive index of the reflecting material. Then, using Brewster's law, find the angle of refraction.

Fundamentals

According to Brewster's law, the maximum polarization occurs when the angle of reflection and angle of refraction make an angle of \(90^{\circ}\) Another statement for Brewster's law is that the tangent of the polarization angle is equal to the ratio of the refractive indices of the contacting mediums. \(\tan \theta_{p}=\frac{n_{2}}{n_{1}}\)

Here, \(\theta_{p}\) is the angle of polarization, \(n_{2}\) is the refracted medium and \(n_{1}\) is the incident medium.

(a) According to Brewster's law as given below:

\(\tan \theta_{p}=\frac{n_{2}}{n_{1}}\)

Rewrite the above equation in terms of \(n_{2}\).

\(n_{2}=n_{1} \tan \theta_{p}\)

Substitute 1 for \(n_{1}\) and \(48^{\circ}\) for \(\theta_{p}\) \(n_{2}=(1) \tan 48^{\circ}\)

\(=1.11\)

Part a

Thus, the refractive index of the reflecting material is 1.11.

Brewster's angle is the angle where the unpolarized light after complete polarization is reflected.The first medium is air and the refractive index of air is 1 .

(b) As the reflected ray is completely polarized, the condition is as given below:

\(\theta_{p}+\theta_{r e f}=90^{\circ}\)

Here, \(\boldsymbol{\theta}_{\text {ref }}\) is the angle of refraction. Rewrite the above relation for the angle of refraction. \(\theta_{r e f}=90^{\circ}-\theta_{p}\)

Substitute \(48^{\circ}\) for \(\theta_{p}\)

\(\theta_{r e f}=90^{\circ}-48^{\circ}\)

\(=42^{\circ}\)

Part \(b\) Thus, when the reflected light is completely polarized, the angle of refraction is \(42^{\circ}\).

According to Brewster's law, the maximum polarization occurs when the angle of reflection and angle of refraction make an angle of \(90^{\circ}\). So, the angle of refraction is the difference between \(90^{\circ}\) and the angle of polarization.


Related Solutions

A beam of light in air is incident at an angle of 24.0° to the surface...
A beam of light in air is incident at an angle of 24.0° to the surface of a rectangular block of clear plastic ( n = 1.46). The light beam first passes through the block and re-emerges from the opposite side into air at what angle to the normal to that surface?
A beam of white light is incident on the surface of a diamond at an angle...
A beam of white light is incident on the surface of a diamond at an angle ?a.(Figure 1) Since the index of refraction depends on the light's wavelength, the different colors that comprise white light will spread out as they pass through the diamond. The indices of refraction in diamond are nred=2.410 for red light and nblue=2.450 for blue light. The surrounding air has nair=1.000. Note that the angles in the figure are not to scale. Part A Calculate vred,...
1) if the angle of incidence is greater than the angle of refraction for a light...
1) if the angle of incidence is greater than the angle of refraction for a light ray, is the speed of light faster in a second material? explain your answer 2) a student needs a 100 ohms resistor for a circuit , but he only has a box of 300 ohms resistor, can the 300 ohms resistor be combined to make a 100 ohms resistor? 3) Explain how can you determine the types of radiation emitted by a nucleus when...
Consider a beam of light passing from air into glass (refractive index 1.5) at an angle...
Consider a beam of light passing from air into glass (refractive index 1.5) at an angle of 30 degrees from vertical. Calculate - The angle of the reflected light - The angle of the refracted light - The intensity of the reflected light - The intensity of the refracted light
Light in a vacuum is incident on a transparent glass slab. The angle of incidence is...
Light in a vacuum is incident on a transparent glass slab. The angle of incidence is 37.0
A beam of light strikes a sheet of glass at an angle of 57.0deg. with the...
A beam of light strikes a sheet of glass at an angle of 57.0deg. with the normal in air. You observe that red light makes an angle of 38.1 degrees with the normal in the glass, while violet light makes a 36.7 degree angle. 1.What are the indexes of refraction of this glass for these colors of light? 2.What are the speeds of red and violet light in the glass?
A light beam strikes a piece of glass at a 53.00 ∘incident angle. The beam contains...
A light beam strikes a piece of glass at a 53.00 ∘incident angle. The beam contains two wavelengths, 450.0 nm and 700.0 nm, for which the index of refraction of the glass is 1.4831 and 1.4754, respectively. Part A What is the angle between the two refracted beams?
Light moves from inside an ice cube to air. At what angle was the light incident upon the ice/air boundary if the refracted angle was 35°?
Question 20 Light moves from inside an ice cube to air. At what angle was the light incident upon the ice/air boundary if the refracted angle was 35°? The index of refraction for the air is 1.0 and 1.4 for the ice.Question 20 options:53°35°12°66°24°Question 203An object is placed 10 cm in front of a concave mirror of focal length 5 cm. The image produced isQuestion 23 options:Virtual and uprightNone of the aboveReal and invertedReal and uprightVirtual and inverted
The critical angle for an air-glass interface is 25.3°. When a light ray in air is...
The critical angle for an air-glass interface is 25.3°. When a light ray in air is incident on the interface, the reflected ray is 100% polarized. What is the angle of refraction of that ray?
A laser beam with vacuum wavelength 582 nm is incident from air onto a block of...
A laser beam with vacuum wavelength 582 nm is incident from air onto a block of Lucite as shown in the figure below. The line of sight of the photograph is perpendicular to the plane in which the light moves. Take θ1 to be 60°. Recall that the index of refraction of air is 1 and Lucite is 1.50. (a) Find the speed of the light in Lucite.. m/s (b) Find the frequency of the light in Lucite.. Hz (c)...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT