As you may have learned when studying the properties of thermal energy, building

Question

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 = 1.50) 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 ?x as the light enters the room. (Use na = 1.00)

Explanation / Answer

from air to first glass:

incident angle.@i = 90-40 = 50 deg

ni = 1 and nr = 1.50

using Snell's law,

ni sin@i = nr sin@r

1 * sin50 = 1.50 sin@r

@r = 30.71 deg

lateral shift of of this ray:

x1 = 32 tan30.71 = 19 mm

shift of virtual ray:

x1' = 32 tan50 = 38.14 mm

now for first glass to air gap:

ray will again make angle 50 deg with normal and shift will not change.

now again for air to glass.

all quantities are same hence shifts of ray will be same.

so shift in path will be

deltax = 2(x1' - x1) = 2(38.14 - 19) = 38.27 mm

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