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 (n_g = 1.46), cach y_g = 42.0 mm thick, separated by an air gap of y_a = 33.6 mm. If light incident on the glass makes an angle of φ = 40.00° with respect to the glass, find the shift in path Δx as the light enters the room. Use n_a = 1.00 for the index of refraction of air. 

Δx= _______ mm

Answer 1

40.00 Ni r 42 mm glass с 33.6 mm A B 40°N air < glass 42 mm r A' B' Ax

The angle of incidence is i = 90 - 40 = 50

i = 50

Using Snell's law , we find the angle of refraction ,

R = sin i / sin r

We know that the ref.index is 1.46

then r = 31.6 . aprox = 32

Now ;

Lateral shift =tsin(i-r)/cosr =tsecr sin(i-r) where t is the thickness of the material and all other are having standar notation.

Substituting we get ,

t = 42 mm

i = 50

r = 32

Then x = [(42 * 10^-3 m) * sin (50 - 32) ]/ cos(32)

x  = 15.3042 mm

P.S.If this helped you please like the answer.Thankyou.

Answer 2