Nelson Science Perspectives 10
1st Edition
ISBN: 9780176355289
Textbook solutions
All Solutions
Section 12-5: Total Internal Reflection
Exercise 1
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For total internal reflection to occur:
1. Light must be travelling from an optically denser medium to an optically less dense medium.
2. Angle of incidence must be greater than the critical angle of the material (optically denser medium).
Exercise 2
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When light is entering an optically less dense medium from an optically denser medium, then the speed of light increases as it does so and therefore it bends away from the angle. As this angle of incidence is increased, the angle of refraction also increases up to the point where the angle of refraction increases to $90text{textdegree}$. At this point, the refracted ray is lying on the boundary of the two mediums. The angle of incidence that produces the angle of refraction of $90text{textdegree}$, is called the critical angle. If the angle of incidence is increased any further, than the ray is no longer refracted, but reflected inside the optically denser medium causing total internal reflection. Since, the refracted ray bends away from the normal on entering an optically less dense medium, this phenomenon is only possible in this scenario and not the other way around.
Exercise 3
Result
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Critical angle of sapphire is $34.4text{textdegree}$, this implies that for angles of incidence $23.7text{textdegree}$ and $31.5text{textdegree}$, the light rays will be refracted, while for angles of incidence $34.7text{textdegree}$ and $53.4text{textdegree}$, the light rays will be internally reflected.
Exercise 4
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Prisms reflect 100$%$ of the light falling on them internally, (if it is greater than their critical angle). This is not possible in a plane mirror because plane mirrors have the tendency to absorb a certain portion of the light incident on them. The silver lining of the mirrors also diminishes over time and this means that either the mirror needs to be repainted or replaced which is not possible is optical devices, therefore it is better to use prisms and they reflect light better and are maintenance free.
Result
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It is better to use prisms and they reflect light better and are maintenance free.
Exercise 5
Solution 1
Solution 2
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The smaller the critical angle of a medium is, the more ability for internal reflection medium will have since the angle of incident ray has to be greater than the critical angle.
Result
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There will be more total internal reflection when the critical angle is smaller.
Step 1
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The angle of the incident ray must be greater than the critical angle for the light to reflect internally. This means that the smaller the critical angle of a medium, the more it has the ability to reflect light internally as compared to a medium with a large critical angle.
Result
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The smaller the critical angle of a medium, the more it has the ability to reflect light internally.
Exercise 6
Solution 1
Solution 2
Result
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Retroreflectors could line the sides of the road so that people can better judge turns in the dark as they will provide more reference points to make turning decisions.
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Retro-reflectors could be placed on the sides of the road since they will provide more referent points so that the drivers can judge turns better while it is dark.
Result
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Those can be put on the sides of the road so that the drivers can judge turns better in the dark.
Exercise 7
Solution 1
Solution 2
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1. Total internal reflection is used in optical fiber to transmit signals in the form of light from one location to another.
Step 2
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2. Total internal reflection in prisms is used in optical devices such as periscope, binoculars and cameras.
Step 3
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3. Total internal reflection is used in automotive sensors to determine parameters like presence of rain.
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Total internal reflection is used:
1. In automotive sensors which can determine several parameters such as presence of rain.
2. In optical fibers in order to transmit signals in the form of light. (internet etc.)
3., TIR in prisms is used in construction of periscope, binoculars, cameras etc.
Result
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1. In automotive sensors which can determine several parameters such as presence of rain.
2. In optical fibers in order to transmit signals in the form of light. (internet etc.)
3., TIR in prisms is used in construction of periscope, binoculars, cameras etc.
Exercise 8
Solution 1
Solution 2
Step 1
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Total internal reflection occurs when light enters an optically less dense medium from an optically denser medium, as a result of which its speed increases and the refracted ray bends away from the normal. This can only be seen in figure b and therefore it is only in b that total internal reflection can occur if the angle of incidence is increased.
Result
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Figure 13 b.
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Since the total internal reflection occurs when light travels from optically denser medium to the less dense one when the speed of light ray increases and it bends away from the normal due to that.
Therefore, we can conclude that only in figure $textit{ Figure 13. b}$ total internal reflection is shown.
Result
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Only in $textit{Figure 13. b}$ total internal reflection is shown.
Exercise 9
Solution 1
Solution 2
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Since total internal reflection occurs when light travels from optically denser medium to the one with less dense which causes change in speed and, therefore, refracted ray of light is being bend away from the normal.
It is clearly shown in $textit{Figure 13. b}$ that when the internal reflection can occurs when the angle of incidence is increased.
Result
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$textit{Figure 13. b}$
Step 1
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Total internal reflection occurs when light enters an optically less dense medium from an optically denser medium, as a result of which its speed increases and the refracted ray bends away from the normal. This can only be seen in figure b and therefore it is only in b that total internal reflection can occur if the angle of incidence is increased.
Result
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Figure 13 b.
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