Question

(1) 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 (ng=1.40), each yg=52.0 mm thick, separated by an air gap of ya=41.6 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 na=1.00 for the index of refraction of air.

(2) The index of refraction of silicate flint glass for red light is 1.620 and for violet light is 1.660 . A beam of white light in this glass strikes the glass–air interface at a 25.10° angle of incidence and refracts out into the air. What is the angular separation between the red and violet components of the spectrum that emerges from the glass?

Answer 1

1)

Using Snell's law,

n1 sin(i) = n2 sin(r)

1 sin(50) = 1.40 sin(r1)

r1 = 33.17°

Shift, L1 = 52 sin(50 - 33.17)/cos(31.17) = 17.59 mm

For glass 2,

1 sin(50) = 1.40 sin(r2)

r2 = 33.17°

Shift, L2 = 52 sin(50 - 33.17)/cos(31.17) = 17.59 mm

Shift, L = L1 + L2 = 35.19 mm

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