A lamp is twice as far in front of a plane mirror as a person is. Light from the

Question

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 degree angle of incidence and reflects from it before reaching the person. The total time for the light to travel this path include 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.

Explanation / Answer

Let the distance of the person from the mirror be 'd '
Now the distance of the lamp from the mirroris 2d

Distance traveled by the light in the direct path is r1=d
Time taken by the light to reach the person in direct path is t1 = r1/c = d/c
c = velocity of light
Now distance traveled by the light to travel in the reflected path is r2 = 2(2d/cos?)
Where '?' angle of incidence of light on the mirror Now time taken by the light to reach the person in the reflected path is t2 = r2/c = 2(2d/cos?)/c Here ?=30 degrees Then t2 = 2(2dcos30) / c =8d/v3c Then ratio of time taken along the reflected path to the time taken along direct path is t2/t1 =  8d/v3c /d/c
        =8/v3         =4.62

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