Finding distance by angle of incident

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SUMMARY

The problem involves calculating the horizontal distance from a lighthouse to a shipwreck based on the angle of incidence of light. The lighthouse is 55 meters above sea level, and the beam strikes the water at an angle of 63 degrees, illuminating a shipwreck located 17 meters deep. Using the tangent function, the horizontal distance to the point directly below the light source is calculated as 110 meters. After applying Snell's Law, the angle of refraction is determined to be 42 degrees, leading to an additional distance of 15 meters, resulting in a total horizontal distance of 125 meters from the lighthouse to the shipwreck.

PREREQUISITES
  • Understanding of trigonometric functions, specifically tangent.
  • Familiarity with Snell's Law for refraction of light.
  • Basic knowledge of significant figures in calculations.
  • Ability to perform calculations involving angles and distances in a physics context.
NEXT STEPS
  • Study the application of Snell's Law in different mediums.
  • Learn about significant figures and their importance in scientific calculations.
  • Explore advanced trigonometric functions and their applications in real-world problems.
  • Investigate the principles of light behavior in various environments, such as underwater optics.
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Students in physics or engineering fields, educators teaching optics and trigonometry, and anyone interested in practical applications of light behavior in different mediums.

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Homework Statement



The light in a lighthouse sits 55 m above sea level. The beam of light strikes the water
at an angle of incidence of 630 and illuminates a shipwreck on the ocean floor. If the
water is 17 m deep, what is the horizontal distance from the lighthouse to the shipwreck?

Homework Equations



tan=opp/adj

n1sinθ1=n2sinθ2

The Attempt at a Solution



tan63=x/55m

x=110m

(1.0)sin(63°)=(1.33)sinθ2

θ2=42

tan(42)=opp/17m
opp=15m

15+110m=125m
 
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aChordate said:

Homework Statement



The light in a lighthouse sits 55 m above sea level. The beam of light strikes the water
at an angle of incidence of 630 and illuminates a shipwreck on the ocean floor. If the
water is 17 m deep, what is the horizontal distance from the lighthouse to the shipwreck?

Homework Equations



tan=opp/adj

n1sinθ1=n2sinθ2

The Attempt at a Solution



tan63=x/55m

x=110m

(1.0)sin(63°)=(1.33)sinθ2

θ2=42

tan(42)=opp/17m
opp=15m

15+110m=125m

Your method is correct, but you do not get the result with three significant digits if you calculate with two digits. The data are given with two digits, use three during the calculations and round off at the end.

ehild
 
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