Question

A photon can travel along any one of the three paths in the accomanying Figure. The inital point and the final point are a height H = 26 cm and distance D = 87 cm away from each other, and there is a window of width d = 29 cm and index of refraction 1.31 placed midway between along the path. Assume the air has index of refraction 1.

Path (a) is a straight line between the starting and ending locations.

Path (b) goes in a horizontal line between until it exits the glass and turns toward the final point

Path (c) Goes diagonally through the air to the midpoint of the glass, then goes horizontally, and finally goes diagonally to the final point.

How long does the light take to get from start to finish for:

Path (a)?
ns

Path (b)?
ns

Path (c)?
ns

Answer 1

Solution H= 26cm ,D=87cm, d=29cm, nz 1:31 = 0.26m =0.87m = 0.29m Pathley S Tano. # C:2-988x8 mg Length of path in air a D-d coso Length of path in medium = a Speed of light in medium, v=ch t=D-d + Coso (c) d Coso =D+cnold Cobo (c) 3-342*10'S - 3-342ns to 0.87+(1:31-1) 0.29 - - 0o87 (2.998*18) Vos?+0.262 Path(b) a (b +d X2 < (B-d) (z . (D-d)/2 011 Cos - Vi / H² + (092 Length of path in air a D-d + Dar es Length of path in medium=d to + pop). is

te 1 (9-87-0:27) + 0.87-029) 7 2.998X108 260.87-0-29)/2 +0.291:31 Voze +60-81-0-2913 20998718 2.998X108 t=30534x10's=30534 ns Path(c) Tan & = Hl2 (D-dyl H Dd Ta D-d Cos = Vco-d²+ H2 Length of path in air = 2 0 . coso Length of path in medium ad t= D-d + d cosocc)' (cin) = (0.87-0.29) 2.998x18x(0-87-0-29) + 0.29X 1031 2.998818 V60-87-020] +0262 t= 3.387x10's= 30387 ns