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Light takes $ {t_1} $ sec to travel a distance $ x $ in a vacuum and the same light takes $ {t_2} $ sec to travel $ 10cm $ in a medium. The critical angle for the corresponding medium will be (A) $ {\sin ^{ - 1}}\left( {\dfrac{{10{t_2}}}{{{t_1}x}}} \right) $ (B) $ {\sin ^{ - 1}}\left( {\dfrac{{{t_2}x}}{{10{t_1}}}} \right) $ (C) $ {\sin ^{ - 1}}\left( {\dfrac{{10{t_1}}}{{{t_2}x}}} \right) $ (D) $ {\sin ^{ - 1}}\left( {\dfrac{{{t_1}x}}{{10{t_2}}}} \right) $
- Critical Angle
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Light Year Calculator
What is light year, how to calculate light years.
With this light year calculator, we aim to help you calculate the distance that light can travel in a certain amount of time . You can also check out our speed of light calculator to understand more about this topic.
We have written this article to help you understand what a light year is and how to calculate a light year using the light year formula . We will also demonstrate some examples to help you understand the light year calculation.
A light year is a unit of measurement used in astronomy to describe the distance that light travels in one year . Since light travels at a speed of approximately 186,282 miles per second (299,792,458 meters per second), a light year is a significant distance — about 5.88 trillion miles (9.46 trillion km) . Please check out our distance calculator to understand more about this topic.
The concept of a light year is important for understanding the distances involved in space exploration. Since the universe is so vast, it's often difficult to conceptualize the distances involved in astronomical measurements. However, by using a light year as a unit of measurement, scientists and astronomers can more easily compare distances between objects in space.
As the light year is a unit of measure for the distance light can travel in a year , this concept can help us to calculate the distance that light can travel in a certain time period. Hence, let's have a look at the following example:
- Source: Light
- Speed of light: 299,792,458 m/s
- Time traveled: 2 years
You can perform the calculation in three steps:
Determine the speed of light.
The speed of light is the fastest speed in the universe, and it is always a constant in a vacuum. Hence, the speed of light is 299,792,458 m/s , which is 9.46×10¹² km/year .
Compute the time that the light has traveled.
The subsequent stage involves determining the duration of time taken by the light to travel. Since we are interested in light years, we will be measuring the time in years.
To facilitate this calculation, you may use our time lapse calculator . In this specific scenario, the light has traveled for a duration of 2 years.
Calculate the distance that the light has traveled.
The final step is to calculate the total distance that the light has traveled within the time . You can calculate this answer using the speed of light formula:
distance = speed of light × time
Thus, the distance that the light can travel in 100 seconds is 9.46×10¹² km/year × 2 years = 1.892×10¹³ km
How do I calculate the distance that light travels?
You can calculate the distance light travels in three steps:
Determine the light speed .
Determine the time the light has traveled.
Apply the light year formula :
distance = light speed × time
How far light can travel in 1 second?
The light can travel 186,282 miles, or 299,792,458 meters, in 1 second . That means light can go around the Earth just over 7 times in 1 second.
Why is the concept of a light year important in astronomy?
The concept of a light year is important in astronomy because it helps scientists and astronomers more easily compare distances between objects in space and understand the vastness of the universe .
Can light years be used to measure time?
No , despite the name, you cannot use light years to measure time. They only measure distance .
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Questions
Light takes time t 1 s to travel a distance X cm in vacuum and the same light takes time t 2 to travel 10X cm in medium. The critical angle for the corresponding medium is
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detailed solution
Correct option is C
Speed of light in medium v d = 10 t 2 [ ∴ r = d t ]
v μ m = 1 sin C
μ m μ v = 1 sin C
sin C = μ r μ m
μ α 1 v ⇒ sin C = v m v r
sin C = 10 t 2 × t 1 1
sin C = 10 t 1 t 2
C = sin − 1 ( 10 t 1 t 2 )
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- If light travels a distance x in time t1 in air and 10x distance in time t2 in a certain medium, then find the critical angle for total internal reflection, of the medium.
Q. If light travels a distance x in time t 1 in air and 10 x distance in time t 2 in a certain medium, then find the critical angle for total internal reflection, of the medium.
S i n − 1 ( t 2 20 t 1 ), s i n − 1 ( t 2 10 t 1 ), s i n − 1 ( t 2 t 1 ), s i n − 1 ( 10 t 1 t 2 ), μ = t 2 10 x t 1 x = 10 t 1 t 2 sin θ c = t 2 /10 t 1 1 = t 2 10 t 1 ⇒ θ c = sin − 1 ( t 2 10 t 1 ).
*3; : 1.500 1.333 aking 3) 6102 4) 6303 carer medium. 11 5. Light takes time to travel a distance x, in medium with us avel a distance cuum and the same light takes time t, to travel a in maximum possi sistance X, in a medium. The critical angle for that 1) -C 41. A points of a water la on the surface ( Xiti X21 depth of the angle medium is 1) sin-X2 t2 2) sin-1 Xt2 1) VE
Light takes t 1 sec to travel a distance x in a vacuum and the same light takes t 2 sec to travel 10 x cm in a medium. The critical angle for the corresponding medium will be
Light takes T 1 sec to travel a distance x In a vacuum and the same light takes T 2 sec to travel 10 c m in a medium. The critical angle for the corresponding medium will be:
Critical angle: when light ray traveling in the denser medium is incident on the rarer medium at an angle of incidence such that the refracted ray grazes out through the interface boundary (∠r=90) then the angle of incidence is called the critical angle. step 1. given data: in the case of vacuum, time= t 1 , distance= x , in the case of a medium, time= t 2 , distance= 10 c m step 2. formula used: sin i c = v c where i c =critical angle, c = velocity of light in vacuum, v = velocity of light in a medium. step 3. explanation: c = velocity of light in vacuum. v = velocity of light in a medium. here, we can clearly see, c = x t 1 , v = 10 t 2 where c , x , v , t 1 a n d t 2 have their usual meanings. also, sin i c = 1 μ = v c = 10 t 2 × t 1 x = 10 . t 1 t 2 . x i c = sin - 1 10 . t 1 t 2 . x hence, the critical angle for the corresponding medium will be, i c = sin - 1 10 t 1 t 2 x ..
COMMENTS
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The final step is to calculate the total distance that the light has traveled within the time. You can calculate this answer using the speed of light formula: distance = speed of light × time. Thus, the distance that the light can travel in 100 seconds is 299,792,458 m/s × 100 seconds = 29,979,245,800 m. FAQs.
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The time taken by the light to travel $ 10cm $ in a medium is taken as $ {t_2} $ . The velocity of light through the medium can be taken as $ v $ $ v = \dfrac{{10}}{{{t_2}}} $ The absolute refractive index can also be expressed as the ratio of the velocity of light in vacuum $ (c) $ to the velocity of light in the medium. i.e.
The final step is to calculate the total distance that the light has traveled within the time. You can calculate this answer using the speed of light formula: distance = speed of light × time. Thus, the distance that the light can travel in 100 seconds is 9.46×10¹² km/year × 2 years = 1.892×10¹³ km.
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The correct answer is speed of light in vacuum vr=xt1 Speed of light in mediumvd=10t2 [∴r=dt] vμm=1sinC μmμv=1sinC sinC=μrμm μα1v⇒sinC=vmvr sinC=10t2×t11 sinC=10t1t2 C=sin−1(10t1t2) ... Light takes time t 1 s to travel a distance X cm in vacuum and the same light takes time t 2 to travel 10X cm in medium. The critical angle for ...
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