1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
pantera1 [17]
3 years ago
8

In which medium does light travel faster: one with a critical angle of 27.0° or one with a critical angle of 32.0°? Explain. (Fo

r both cases, air is the second medium.)
Physics
1 answer:
Eddi Din [679]3 years ago
4 0

Answer:

Among those two medium, light would travel faster in the one with a reflection angle of 32^{\circ} (when light enters from the air.)

Explanation:

Let v_{1} denote the speed of light in the first medium. Let v_{\text{air}} denote the speed of light in the air. Assume that the light entered the boundary at an angle of \theta_{1} to the normal and exited with an angle of \theta_{\text{air}}. By Snell's Law, the sine of \theta_{1}\! and \theta_{\text{air}}\! would be proportional to the speed of light in the corresponding medium. In other words:

\displaystyle \frac{v_{1}}{v_{\text{air}}} = \frac{\sin(\theta_{1})}{\sin(\theta_{\text{air}})}.

When light enters a boundary at the critical angle \theta_{c}, total internal reflection would happen. It would appear as if the angle of refraction is now 90^{\circ}. (in this case, \theta_{\text{air}} = 90^{\circ}.)

Substitute this value into the Snell's Law equation:

\begin{aligned}\frac{v_{1}}{v_{\text{air}}} &= \frac{\sin(\theta_{1})}{\sin(\theta_{\text{air}})} \\ &= \frac{\sin(\theta_{c})}{\sin(90^{\circ})} \\ &= \sin(\theta_{c})\end{aligned}.

Rearrange to obtain an expression for the speed of light in the first medium:

v_{1} = v_{\text{air}} \cdot \sin(\theta_{1}).

The speed of light in a medium (with the speed of light slower than that in the air) would be proportional to the critical angle at the boundary between this medium and the air.

For 0 < \theta < 90^{\circ}, \sin(\theta) is monotonically increasing with respect to \theta. In other words, for \!\theta in that range, the value of \sin(\theta)\! increases as the value of \theta\! increases.

Therefore, compared to the medium in this question with \theta_{c} = 27^{\circ}, the medium with the larger critical angle \theta_{c} = 32^{\circ} would have a larger \sin(\theta_{c}). such that light would travel faster in that medium.

You might be interested in
25 Points PLEASE I need Help
olga55 [171]

Answer:nah u took my points I take urs

Explanation:

6 0
3 years ago
Include units with all of your answers. A 1.84 kg bucket full of water is attached to a 0.76 m long string.
aleksandrvk [35]
<span>c. What is the magnitude of the tension in the string at the bottom of the circle if you are swinging it at 3.37 m/s? </span>
7 0
3 years ago
A star is held together by:gravitynuclear fissionnuclear fusionacceleration
alina1380 [7]
Nuclear fusion in the core tries to blow the star apart. Gravity holds it together. Whoever designed that system really knew what he was doing. I'm​ kinda grateful to him.
6 0
3 years ago
How does friction make it possible for you to walk across the floor?
Tema [17]

if we are walking on a perfectly smooth ground which has no friction our force would simply cancel out the force reverted by the ground and we would fall.

We need it to help push out feet off the ground

Hope those helps :)

5 0
3 years ago
What is the net force acting upon this object? *
AnnZ [28]

2 N Right

.. .. .. .. .. .. .. ..

4 0
3 years ago
Read 2 more answers
Other questions:
  • A baseball player catches a ball that has a mass of .25 kg that was traveling at 40 m/s. The ball came to stop in her baseball g
    12·1 answer
  • Which group of components is common to the circulatory systems of most living animals? A. arteries, veins, capillaries B. vessel
    14·1 answer
  • Cuál es el tiempo empleado por una moto que alcanza una velocidad final de 100km/h partiendo del reposo y lo hace a una acelerac
    8·1 answer
  • When two or more atoms combine into a chemical compound, the force of attraction holding the atoms together is known as a ...
    5·1 answer
  • The time required for the passage of one wavelength is the: period frequency amplitude velocity
    14·2 answers
  • A student standing on a stationary skateboard tosses a textbook with a mass of mb = 1.5 kg to a friend standing in front of him.
    6·1 answer
  • 400 Kelvin to degrees Celsius​
    10·2 answers
  • A sound wave has a frequency of 300 Hz. If the wavelength is .50 m, then what is the speed of
    8·1 answer
  • Your friend clams that objects do not have to be thouching for a magnetic force to cause motion. How would you support your frie
    10·1 answer
  • 3) Calculate the kinetic energy of a 7 kg mass traveling at a velocity of 4 m/sec.
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!