Calculating Refraction Time in Water: Physics Homework Help

In summary, the question asks how long it takes for light to cross 2.3 km of water with an index of refraction of 1.32, given that the angle of incidence is 69 degrees. The answer is 15.34 microseconds, calculated using the equation h=d/cosθ and the fact that the speed of light in water is v=c/n.
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Homework Statement


Light is originally traveling through air and then enters water with an index of refraction of 1.32. Angle in air at interface is 69 degrees with respect to normal. If thickness of water is 2.3 km, how long does it take in microseconds (1 x 10-6 s) to cross water? Hint: light does not travel straight across water because it is refracted by water. Answer is 15.34.

Homework Equations


nasin[tex]\phi[/tex]a=nbsin[tex]\phi[/tex]b
n=c/v

The Attempt at a Solution


(1)sin69=1.32sin[tex]\phi[/tex]b
[tex]\phi[/tex]b=sin-1(sin69/1.32)=45.01
cos[tex]\phi[/tex]b=d/h
h=d/cos[tex]\phi[/tex]b
nv=c
v=h/t=c/n
t=hn/c=dn/ccos[tex]\phi[/tex]b x 106=(2.3 x 103m*1.32)/(3 x 108cos45.01) x 106=14.31
I am not certain what I am doing wrong, but that answer is incorrect.
 
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  • #2


It looks correct.

ehild
 

FAQ: Calculating Refraction Time in Water: Physics Homework Help

What is refraction?

Refraction is the phenomenon of light bending when it passes through a different medium. This can occur when light passes through substances with different densities, such as air, water, or glass.

How does refraction work?

Refraction is caused by a change in the speed of light as it passes through different materials. When light enters a denser medium, it slows down and bends towards the normal line. When it exits a denser medium, it speeds up and bends away from the normal line.

What is the law of refraction?

The law of refraction, also known as Snell's law, states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the speed of light in the first medium to the speed of light in the second medium.

How does refraction affect the appearance of objects?

Refraction can cause objects to appear distorted or shifted when viewed through different mediums. For example, objects in water may appear closer or larger due to the bending of light as it passes through the water.

What are some real-life applications of refraction?

Refraction has many practical applications, such as in the design of lenses for eyeglasses, cameras, and microscopes. It is also used in the construction of optical instruments such as telescopes and binoculars. In addition, refraction is important in understanding the behavior of light in the atmosphere, which affects weather patterns and the appearance of objects in the sky.

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