**47. ssm A lamp is twice as far in front of a plane mirror as a person is. Light from the lamp reaches the person via two paths, reflected and direct. It strikes the mirror at a 30.0° angle of incidence and reflects from it before reaching the person. The total time for the light to travel this path includes the time to travel to the mirror and the time to travel from the mirror to the person. The light also travels directly to the person without reflecting. Find the ratio of the total travel time along the reflected path to the travel time along the direct path.

 

Diagram shows us the relevant information.  The problem asks for the ratio of the time for two paths of light.

 

Time for light to travel a distance L is given by usual kinematics for an object traveling at constant speed.

So the ratio is

 

To get the path lengths, use the triangles formed in the diagram.  The three paths are  hypotenuses for three right triangles.

 

 

 

 

Now we get the two y distances by using the tangent function remember q is 30°

 

So we know

 

 

Plug these into the equations above

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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This page last updated on June 30, 2018