Suppose a photon leaves the origin traveling along the vector v0 =< 1, 3, −1 >...

Suppose a photon leaves the origin traveling along the vector v0 =< 1, 3, −1 > towards a mirror lying on the plane 2x + 3y − 5z = 30.

a) Find a vector function r(t) that describes the path of the photon as it travels towards the mirror.

b) Find the value of t0 and the coordinates of the point (x0, y0, z0) where the photon hits the mirror.

c) Find the velocity vector r 0 (t0) of the photon when it hits the mirror.

d) Find a vector perpendicular to the mirror.

e) Calculate the vector the photon will be traveling along after it reflects.

f) Find a vector function for the path of the photon after it bounces off the mirror which incorporates that the photon is at the mirror at the point (x0, y0) at t = t0 from part (b).

g) Calculate the angle between the incoming vector and the normal vector and verify that it equals the angle between the reflected vector and the normal vector in the opposite direction.

Expert Solution

genius_generous answered 2 years ago

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