Purchase Solution

Optics: Point of Refraction

Not what you're looking for?

Ask Custom Question

Given a hemisphere of radius r defined by:

x = r*cos(a)
y = r*sin(a) where -pi/2 <= a <= pi/2

If the hemisphere describes a boundary between two interfaces having indices of refraction n (outside the hemisphere) and m (inside the hemisphere) and assuming the light strikes the hemisphere at point {x,y} with angle a (meaning the light's path is perfectly vertical outside the hemisphere), then it can be shown from Snell's law [n*sin(a) = m*sin(b)] and geometrical reasoning that the equation describing the path the light takes inside the hemisphere (i.e. all {p,q} such that x <= p <= (x - s*y) and 0 <= q <= y) is:

p-x = s*(q-y)
s = tan(a-b)
b = arcsin(n*sin(a)/m)

The problem:

Given any {p,q} inside the hemisphere calculate the point or points {x,y} that cause the refracted light to pass through {p,q}.

Stated another way:

Given any {p,q} inside the hemisphere calculate the angle or angles a that cause the refracted light to pass through {p,q}.

Purchase this Solution

Solution Summary

This solution solves the expressions isolating x and y. The optics for point of refraction are determined.

Solution Preview

point (x,y) lies on the hemisphere, therefore,
x^2 + y^2 = r^2 .....(1)
p-x = s*(q-y)
=> x = p - s*(q-y) = (p - sq) + sy ....(2)

Hence, ...

Solution provided by:
  • BEng, Allahabad University, India
  • MSc , Pune University, India
  • PhD (IP), Pune University, India
Recent Feedback
  • " In question 2, you incorrectly add in the $3.00 dividend that was just paid to determine the value of the stock price using the dividend discount model. In question 4 response, it should have also been recognized that dividend discount models are not useful if any of the parameters used in the model are inaccurate. "
  • "feedback: fail to recognize the operating cash flow will not begin until the end of year 3."
  • "Answer was correct"
  • "Great thanks"
  • "Perfect solution..thank you"
Purchase this Solution

Free BrainMass Quizzes
Variables in Science Experiments

How well do you understand variables? Test your knowledge of independent (manipulated), dependent (responding), and controlled variables with this 10 question quiz.

Introduction to Nanotechnology/Nanomaterials

This quiz is for any area of science. Test yourself to see what knowledge of nanotechnology you have. This content will also make you familiar with basic concepts of nanotechnology.

Intro to the Physics Waves

Some short-answer questions involving the basic vocabulary of string, sound, and water waves.

Classical Mechanics

This quiz is designed to test and improve your knowledge on Classical Mechanics.

Basic Physics

This quiz will test your knowledge about basic Physics.