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 = 1.50), each y_g = 32.0 mm thick, separated by an air gap of y_a = 25.6 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

Here angle of incidence i = 90 -40 degree = 50 degree

angle of refraction r = arcsin(n_a sin 50 degree / n_g) = arcsin( sin 50 degree/1.5) = 30.71 degree

lateral displacement = (yg+yg)*sec r * sin (I-r)

= [32+32]*sec 30.71 degree * sin (50 - 30.71) degree

= 64*sec 30.71 degree *sin 19.29 degree

= 24.59 mm answer