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Math Help - maximum radius of circle above water

  1. #1
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    maximum radius of circle above water

    A point source of light is submerged 2.2 m below the surface of a lake and emits rays in all directions. On the surface of the lake, directly above the source, the area illuminated is a circle. What is the maximum radius that this circle could have?

    in meters.

    Not sure how this can be calculated if I only have the distance of 2.2 meters straight down?

    thanks for anyone who can explain, what i'm missing here.
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  2. #2
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    Quote Originally Posted by rcmango View Post
    A point source of light is submerged 2.2 m below the surface of a lake and emits rays in all directions. On the surface of the lake, directly above the source, the area illuminated is a circle. What is the maximum radius that this circle could have?

    in meters.

    Not sure how this can be calculated if I only have the distance of 2.2 meters straight down?

    thanks for anyone who can explain, what i'm missing here.
    The light rays pass from the optical dense medium into the optical light medium. Therefore the angle of refraction will be greater than the angle of incidence. The limit angle - that means the angle of refraction is 90 - is calculated by:

    \sin(\alpha) = \frac1n . In this case with n = 1.33 you get \alpha = 48.75^\circ

    Therefore the radius on the surface of water where you can see the light is:

    r=2.2\ m\cdot \tan(48.75^\circ) \approx 2.51\ m
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  3. #3
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    Okay, thankyou for pointing out the equation for the radius, I tried to set up the equation using snells law, and I didn't think about tangent.

    thanks.
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