Question

# Building contractors often install double-glazed windows to prevent thermal energy (heat) from entering or exiting a...

Building contractors often install double-glazed windows to prevent thermal energy (heat) from entering or exiting a building. In addition to being effective insulators, such windows present interesting optical effects. In the figure, a double-glazed window consists of two identical panes of glass ( ?g=1.46 ), each ?g=22.0 mm thick, separated by an air gap of ?a=17.6 mm . If light incident on the glass makes an angle of ?=40.00∘ with respect to the glass, find the shift in path Δ? as the light enters the room. Use ?a=1.00 for the index of refraction of air.

we are given angle of incidence with respect to glass, but it should be with respect to normal,

so,we can use Snell's law

n1sin1 = n2 sin2

where 1 is for air and 2 is for glass

so,

1 * sin (90 - 40) = 1.46 * sin 2

solve for 2, we get

2 = 31.647 degree

now, light travels through the glass and there is some shift which can be found as

x = t * sin ( 90 - 40 - 31.647) / cos 31.647

where t is thickness of glass

so,

x = 22 * sin 18.35 / cos 31.647

x = 8.137 mm

then there will be no shift while in air

then comes the second glass, as everything is same,

shift will be same

so,

total shift = 8.137 + 8.137 = 16.274 mm

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