(660 nm) and violet (410 nm) wavelengths travels from air, through a flat piece

Question

(660 nm) and violet (410 nm) wavelengths travels from air, through a flat piece of crown glass 2.48 cm thick, and then back to air.

(a) If the beam has an angle of incidence of 24.4° 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.)

____________ Can you write Snell's law for red light as it enters and exits the glass? How does the angle of refraction into glass at the air-glass interface compare to the angle of incidence in glass at the glass-air interface?°

violet   

Please help? I'm not sure what I'm doing wrong, I keep getting the wrong answer.

Help would be much appreciated.

red    

____________ Can you write Snell's law for red light as it enters and exits the glass? How does the angle of refraction into glass at the air-glass interface compare to the angle of incidence in glass at the glass-air interface?°

violet   

____________
Can you write Snell's law for red light as it enters and exits the glass? How does the angle of refraction into glass at the air-glass interface compare to the angle of incidence in glass at the glass-air interface?°

Explanation / Answer

an angle of incidence= 24.4° in air

Refractive index of red light in crown glass=1.512

Refractive index of violet light in crown glass=1.530

From snells law we know that

n1/n2=sinr/sini

r=reflected angle

i=angle of incidence

So,1.512/1.53=sinr/sin24.4

r=24.09o

angle of disperison,24.4-24.09=0.305

2)violet beam strike the bottom of the glass at 410 nm*tan(24.09) =183.31 nm

and the red beam strikes at 660 nm*tan(24.4) =299.38 nm

So the difference is 299.38-183.31 = 116.07 nm0.114cm wide

3) when the beam leaves the glass they both will be refracted back at 24.4o

So the distance across the beam will be the separation distance times the cos(24.4o)

thickness,d=displacement*cos(angle of refraction)

d= 116.07 nm*cos(24.40) = 105.71 nm is the thickness of the glass

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