Solve Huygens' Principle: Find Time & Angle at Interface

[Ophelia_S2]

Homework Statement

a)What is the time t_B it will take for point B of the wavefront to encounter the vacuum/material interface?
Express your answer numerically to two decimal places in units of t_1 (the time it takes light to travel a distance d in a vacuum).

Homework Equations

n=c/v ; v = c/n

The Attempt at a Solution

uh..basically what i did for part a) i set sin(55 degree) = X/d where x is just a arbitary variable i used. Then let d*sin(55 degree) = x. here in the question it state it takes time t_1 to let speed of light travel a distance of d. so i let d = t_1, which will give me an answer of a value corrospond to t_1. However, after i plug in the number i am only getting 1.43(round off) and when i sub them into the system it says error. Most of time if the answer is close enough it will give me a feed back.. but i don't really know what i have done is wrong.. please someoen help me here..

Homework Statement

b)What is the new angle theta at which point C of the wavefront is propagating (relative to a line perpendicular to the vacuum/material interface)? Try to use the fact that you have a spherical wavefront propagating from t=0 at the point where C met the vacuum/material interface until time t_B when the wavefront at point B reached the interface.
Express your answer in terms of inverse trig functions and n (idex refreation i believe).

Homework Equations

d_c=(c*t_b)/n (this comes from part of the question i answer which is correct, and i believe
i suppose to sub the number d_c with those value to get my answer express for part b)

The Attempt at a Solution

btw, for part b) it's similar geometric problem and my attemps are the follow. set r = d_c, cos(theta) = r/a where a is the arbitary variable i use for hyp of the trig triangle. and a = r/cos(theta. Further more sin(35 degree) = d/a and a=d/sin(35 degree). i set both side equal and try to get an expression which work out to be d cos(theta) = r sin(35 degree). However when i sub the number from above equation in, i end up canceling everything and left with inverse cos ( sin 35 degree). can someone please help me out..this question are confusing, and i don't know how i going to approach it.

P.S Thanks to anyone who can give me some tips, mean while i think i will keep trying..the graph i attach to this question is a given graph that relevant for both question. sorry for any unclear part, this is my first time posting..

 

[vela]

You are clearly referencing additional information since you appear to be pulling numbers out of thin air. We don't know what information was given nor what any of the symbols mean. It's impossible to know what was expected without this additional information. That's why we ask that you please post the complete problem statement when seeking help.