Question 15 of 38 Map Sapling Learning macmillan leaming As you may have learned

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Question 15 of 38 Map Sapling Learning macmillan leaming As you may have learned when studying the properties of thermal energy, building contractors often install double-glazed windows to prevent thermal energy ("heat") from entering/exiting the building Although effective as insulators, such windows present interesting optical effects In the figure, a double-glazed window comprises two identical panes of glass (ng- 1.44) separated by an air gap. If the light encounters the glass at an angle of 40.00° with respect to the glass, find the shift in path as the light enters the room. (Use na-1.00) 40.00° Number m im 62.0 mm glass 49.6 mnm air 62.0 mm glass Ar Previous O Check Answer Next Exit Y Hint

Explanation / Answer

total shift in path=shift at first glass air interface + shift at second glass air interface

shift at first glass air interface:

incident angle=90-40=50 degrees

let angle of refraction be theta.

then using snell's law:

1*sin(50)=1.44*sin(theta)

==>theta=32.14 degrees

angle made by the refracted ray with the dotted line =50-32.14=17.86 degrees

length of the the refracted ray inside glass=62 mm/cos(32.14)=73.221 mm

drawing a perpendicular from the point where refracted ray meet the glass-air interface onto the dotted line,

sin(17.86)=shift between two paths/73.221 mm

==>shift between two paths=22.456 mm

using similar approach for the second refraction at glass-air interface,

shift between two paths=22.456 mm

so total shift achieved=22.456+22.456=44.912 mm

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