solutionhw1 - Solutions to Homework Set 1 1 Snellius’ law...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Solutions to Homework Set 1 1) Snellius’ law : Parts a) and b) are trivial, so I will not write out the solutions. Part c) has two sub-parts: i) Setting the variation of F 1 [ y ] to zero gives d dx n ( x ) y √ 1 + y 2 ! = 0 . Now elementary calculus tells us that y = tan θ , where θ is the angle between the light ray and the x-axis. The x-axis is, however, for this geometry, the normal to the planes of constant n ( x ). Thus we have θ = ψ , where ψ is the angle of incidence as it is usually defined in optics. Using the standard trig identities sec 2 θ- tan 2 θ = 1, and sec θ = 1 / cos θ , we reduce our equation to d dx n ( x ) sin ψ = 0 , or n ( x ) sin ψ = const. This last equation is the usual form of Snell’s law. ii) For F 2 [ y ] we can use the first integral to deduce directly that n ( y ) y 2 √ 1 + y 2- n ( y ) q 1 + y 2 = const., or, collecting terms, n ( y ) √ 1 + y 2 = const....
View Full Document

{[ snackBarMessage ]}

Page1 / 3

solutionhw1 - Solutions to Homework Set 1 1 Snellius’ law...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online