From the top of a tall building, a gun is fired. The bullet leaves the gun at a speed of 340 m/s, parallel to the ground. As the
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20) When light passes from air to glass and then to air
21) When a light ray enters a medium with higher optical density, it bends towards the normal
22) Index of refraction describes the optical density
23) Light travels faster in the material with index 1.1
24) Glass refracts light more than water
25) Index of refraction is
26) Critical angle: [/tex]
27) Critical angle is larger for the glass-water interface
Explanation:
20)
It is possible to slow down light and then speed it up again by making light passing from a medium with low optical density (for example, air) into a medium with higher optical density (for example, glass), and then make the light passing again from glass to air.
This phenomenon is known as refraction: when a light wave crosses the interface between two different mediums, it changes speed (and also direction). The speed decreases if the light passes from a medium at lower optical density to a medium with higher optical density, and viceversa.
21)
The change in direction of light when it passes through the boundary between two mediums is given by Snell's law:
with
are the refractive index of 1st and 2nd medium
are the angle of incidence and refraction (the angle between the incident ray (or refracted ray) and the normal to the boundary)
The larger the optical density of the medium, the larger the value of n, the smaller the angle: so, when a light ray enters a medium with higher optical density, it bends towards the normal.
22)
The index of refraction describes the optical density of a medium. More in detail:
- A high index of refraction means that the material has a high optical density, which means that light travels more slowly into that medium
- A low index of refraction means that the material has a low optical density, which means that light travels faster into that medium
Be careful that optical density is a completely different property from density.
23)
As we said in part 22), the index of refraction describes the optical density of a medium.
In this case, we have:
- A material with refractive index of 1.1
- A material with refractive index of 2.2
As we said previously, light travels faster in materials with a lower refractive index: therefore in this case, light travels more quickly in material 1, which has a refractive index of only 1.1, than material 2, whose index of refraction is much higher (2.2).
24)
Rewriting Snell's law,
(1)
For light moving from air to water:
is the index of refraction of air
is the index of refraction ofwater
In this case,
For light moving from air to glass,
is the index of refraction of glass
And so
From eq.(1), we see that the angle of refraction is smaller in the 2nd case: so glass refracts light more than water, because of its higher index of refraction.
25)
The index of refraction of a material is
c is the speed of light in a vacuum
v is the speed of light in the material
So, the index of refraction is inversely proportional to the speed of light in the material:
- The higher the index of refraction, the slower the light
- The lower the index of refraction, the faster the light
26)
From Snell's law,
We notice that when light moves from a medium with higher refractive index to a medium with lower refractive index, , so
, and since
cannot be larger than 1, there exists a maximum value of the angle of incidence
(called critical angle) above which refraction no longer occurs: in this case, the incident light ray is completely reflected into the original medium 1, and this phenomenon is called total internal reflection.
The value of the critical angle is given by
For angles of incidence above this value, total internal reflection occurs.
27)
Using:
For the interface glass-air,
The critical angle is
For the interface glass-water,
The critical angle is
So, the critical angle is larger for the glass-water interface.
Learn more about refraction:
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Answer: The height (position) of the ball and the acceleration due gravity
Explanation:
In this case we are taking about gravitational potential energy, which is the energy a body or object possesses, due to its position in a gravitational field. In this sense, this energy depends on the relative height of an object with respect to some point of reference and associated with the gravitational force.
In the case of the Earth, in which the gravitational field is considered constant, the gravitational potential energy will be:
Where:
is the mass of the ball
is the acceleration due gravity (assuming the ball is on the Earth surface)
is the height (position) of the ball respect to a given point
Note the value of the gravitational potential energy is directly proportional to the height.