In the figure, a double-glazed window comprises two identical panes of glass (ng

Question

In the figure, a double-glazed window comprises two identical panes of glass (ng = 1.40) 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 In the figure, a double-glazed window comprises two identical panes of glass (ng 1.40) 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 as the light enters the room. (Use na-1.00) Number 40.000 32.0 mm glass Tools x 102 25.6 mm air glass Ar

Explanation / Answer

Here, the shift in path occurs in two parts, first through first glass slab, then through second glass slab. There is no shift in air.

Angle the light makes with glass while entering the glass is given as 40 degree with surface, but with the normal to glass air interface, it is 90-40=50 degrees

Now, using the snell's law , at first glass-air surface, na*sin50=ng*sin(theta) {here, theta is the angle the light makes with the same normal described above, when light has entered the glass}

So, 1*0.766=1.4*sin(theta)

So, theta= 33.17 degree.

Now, when light exits first glass, using the relation for shift which is d ={t/cos r}*sin (i-r)

where d= shift

t=thickness of glass=32mm

i=angle of incidence= 50 degree

r=angle of refraction=33.17 degree

Which gives d= 32*sin(50-33.17)/cos(33.17)= 11.067mm.

Now, as the air emerges out in the path parallel to its initial path, and na=1 and ng=1.4, so applying snell's law again, at second glass-air surface,

1*0.766=1.4*sin(theta)

Which gives theta= 33.17 degrees.

Now again using the relation for shift,

d ={t/cos r}*sin (i-r)

where d= shift in second glass

t=thickness of second glass=32mm

i= incidence angle= 50 degrees

r =refraction angle= 33.17 degrees

Which gives d= 32*sin(50-33.17)/cos(33.17)= 11.067mm.

So, shift in path x as the light enters the room = 11.067+11.067= 22.134mm

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