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 efects. In the figure, a double-glazed window comprises two identical panes of glass (n_g = 1.46) separated by an air gap. If the light encounters the glass at an angle of 40.00degree with respect to the glass, find the shift in path Deltax as the light enters the room. (Use n_a = 1.00)

Explanation / Answer

We know that the lateral displacement S or shift of thickness of slab "t" with incident angle i is given by

S =(t/Cosr) sin(i-r)

Now r can be obtained from the Snells law

n = sini/sinr or r =sin-1(sini/n)

Now from the figure both the slabs are identical we get by adding

Deltax =S+S

Now t =22mm, i =50degrees and 40degrees with the glass , n =1.46

Then r =sin-1(sini/n) =31.647degrees

Now S =(t/cosr)sin(i-r)

          =(22/cos(31.647)*sin(50-31.647) =8.1353mm

Now the total shift in the path is DeltaX =S+S =8.1353mm+8.1353mm =16.270mm

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