A beam of light containing red (660 nm) and violet (410 nm) wavelengths travels

Question

A beam of light containing red (660 nm) and violet (410 nm) wavelengths travels from air, through a flat piece of crown glass 2.32 cm thick, and then back to air.

(a) If the beam has an angle of incidence of 41.6° in air, determine the angle at which the two colors of light emerge from the crown glass. The index of refraction respectively for red and violet light in crown glass is 1.512 and 1.530. (Enter a number to three decimal places.)

(b) Determine the distance separating the red and violet light as it emerges from the glass.

Explanation / Answer

In case of light passing through rectangular slab or flat slab, angle of incidence is equal to angle of emergence.
Hence both red and violet color light emerge from glass at same angle, that is 41.6 o .

Distance travelled by light, along normal to thickness of glass
y = t tan(r) ....1( t is thickness of glass and r is angle of refraction of light inside the glass)
using snell's law we have
sin(i) = n sin(r) ........2 ( n is index of refraction of glass)
from 1 and two
y = t sin(i) / ( n2 - sin2(i) )1/2
for red color
yr = 1.134 cm
for violet color
yv = 1.117 cm
Hence distance seprating two lights = 1.134 - 1.117 = 0.017 cm

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