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)

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 es dorto such ewindown gresennfrestng opnical eifiecies ting the building. 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) 40.00 Number 32.0 mm glass 25.6 mm air 32.0 mm glass Ar

Explanation / Answer

incident angle i1= 90 - 40 = 50 deg

using snell's law to find refractive angle , r1

ni sini = nr sinr

1 * sin50 = 1.50 * sinr1

r1 = 30.71 deg

length of ray L1 through glass slab, L1 = d1 / cosr1

L1 = 32mm / cos(30.71) = 62.66 mm

then ,

sin(50 - 30.71) = deltaX1 / L

sin19.3 = deltaX1 / 62.66

deltaX1 = 20.7 mm

and same shift will be produced by second slab.

deltaX = 2 deltaX1 = 41.4 mm

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