Therefore the time taken by a laser game to travel a distance of 5 km underwater having a refractive index of 4/3 will be equal to 2.22 × 10⁻⁵ seconds.
In an undersea environment with a refractive index of 4/3, a laser game will traverse 5 kilometres in 2.22 105 seconds.
Given:
The required distance (d) is 5 kilometres.
The medium's refractive index is (n) = 4/3.
To Locate:
the amount of time it takes a laser beam with a 4/3 refractive index to traverse 5km underwater.
Solution:
The required distance (d) is 5 kilometres or 5000 metres.
The medium's refractive index is (n) = 4/3.
In vacuum, light travels at a speed of 3 108 m/s.
The formula for the speed of light in a substance with a refractive index of 'n' is as follows:
Determining the light's speed in glass:
The distance to be travelled (d) = 5 km = 5000 m
The speed of light in water (v) = 2.25 × 10⁸ m/s
Therefore the time taken by a laser game to travel a distance of 5 km underwater having a refractive index of 4/3 will be equal to 2.22 × 10⁻⁵ seconds.
Answers & Comments
Correct Question: Calculate the time taken by a laser game to travel a distance of 5 km underwater having a refractive index of 4/3.
Answer: The time taken by a laser game to travel a distance of 5 km underwater having a refractive index of 4/3 will be equal to 2.22 × 10⁻⁵ seconds.
Given:
The distance to be travelled (d) = 5 km
The refractive index of the medium (n) = 4/3
To Find:
The time taken by a laser beam to travel a distance of 5 km underwater which has a refractive index equal to 4/3.
Solution:
The distance to be travelled (d) = 5 km = 5000 m
The refractive index of the medium (n) = 4/3
→ The speed of light in Vaccum is 3 × 10⁸ m/s
→ The speed of light in a medium which has a refractive index equal to 'n' is given as:
[tex]\boldsymbol{\therefore Speed\:of\:light\:in\:the\:medium=\frac{Speed\:of\:Light\:in\:Vaccum}{Refractive\:index(n)} }[/tex]
→ Calculating the speed of light in glass:
[tex]\boldsymbol{\therefore Speed\:of\:light\:in\:water=\frac{3\times10^{8} }{(4/3)} }\\\\\boldsymbol{\therefore Speed\:of\:light\:in\:water=3\times\frac{3\times10^{8} }{4} }\\\\\boldsymbol{\therefore Speed\:of\:light\:in\:water=2.25\times10^{8}\:m/s }[/tex]
The distance to be travelled (d) = 5 km = 5000 m
The speed of light in water (v) = 2.25 × 10⁸ m/s
[tex]\boldsymbol{\therefore Time\:taken=\frac{Distance(d)}{Speed(v)} }\\\\\boldsymbol{\therefore Time\:taken=\frac{5000}{2.25\times10^{8} } }\\\\\boldsymbol{\therefore Time\:taken=2222.22\times10^{-8} seconds} }\\\\\boldsymbol{\therefore Time\:taken=2.22\times10^{-5} seconds} }[/tex]
Therefore the time taken by a laser game to travel a distance of 5 km underwater having a refractive index of 4/3 will be equal to 2.22 × 10⁻⁵ seconds.
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Answer:
In an undersea environment with a refractive index of 4/3, a laser game will traverse 5 kilometres in 2.22 105 seconds.
Given:
The required distance (d) is 5 kilometres.
The medium's refractive index is (n) = 4/3.
To Locate:
the amount of time it takes a laser beam with a 4/3 refractive index to traverse 5km underwater.
Solution:
The required distance (d) is 5 kilometres or 5000 metres.
The medium's refractive index is (n) = 4/3.
In vacuum, light travels at a speed of 3 108 m/s.
The formula for the speed of light in a substance with a refractive index of 'n' is as follows:
Determining the light's speed in glass:
The distance to be travelled (d) = 5 km = 5000 m
The speed of light in water (v) = 2.25 × 10⁸ m/s
Therefore the time taken by a laser game to travel a distance of 5 km underwater having a refractive index of 4/3 will be equal to 2.22 × 10⁻⁵ seconds.
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