Question

In: Physics

Suppose a photon starts at the point (−12, 9) along the vector <−4, −3> towards a...

Suppose a photon starts at the point (−12, 9) along the vector <−4, −3> towards a mirror lying on the x-axis (the line y = 0).

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) where the photon hits the mirror.

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

d) Find a vector perpendicular to the mirror (this is the normal vector ).

e) Use the formula above to 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) If you haven’t done so already, draw a picture which incorporates all of your work from the previous steps depicting how the photon bounces off the mirror.

h) In your own words (and in complete sentences), explain what in part (e) you needed to use the velocity vector r 0 (t0) of the photon as the incoming vector and not the position vector r(t0).

Solutions

Expert Solution

genius_generous answered 2 years ago
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