Question

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.

Answer 1

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