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 (n_g = 1.44) separated by an air gap. If the light encounters the glass at an angle of 40.00 degree with respect to the glass, find the shift in path Ax as the light enters the room. (Use n_a = 1.00)

Explanation / Answer

here,

In terms of the incidence angle i , the slab thickness d and the refraction index n , I have found that the lateral shift x is given by

x = (d/n^2) * sin(i)*sqrt(n^2 + sin^2(i) * (sqrt(n^2 sin^2(i)) - cos(i))

i = 40 degree

d = 0.042 m

n = 1.44

so ,

the lateral shift from double gaized window , x' = 2 * x

x' = 2 * (d/n^2) * sin(i)*sqrt(n^2 + sin^2(i) * (sqrt(n^2 sin^2(i)) - cos(i))

x' = 2 * ( 0.042/1.44^2) * sin(40) * sqrt(1.44^2 + (sin(40))^2) * ( sqrt( 1.44^2 - (sin(40))^2 ) - cos(40))

x' = 0.02146 m

x' = 21.46 mm

the shift in path of light is 21.46 mm

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