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 2.26 cm thick, and then back to air.

(a) If the beam has an angle of incidence of 24.8° 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.)

red

violet

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

Explanation / Answer

Part A)

From Snell's Law, the angle it enters will be the angle it exits.The system acts like a glass slab where angle of incidence = angle of emergence hence for both it will still be 24.8o

Part B)

But inside the glass, they will have different angles

For red

n1(sin i) = n2(sin r)

1(sin 24.8) = 1.512(sin r)

r = 16.1o

The distance horizontally it travels is from the tangent function

tan(16.1) = x/2.26

x = 0.6526 m

Next

for violet

1(sin 24.8) = 1.530(sin r)

r = 15.91o

The distance horizontally it travels is from the tangent function

tan(15.91) = x/2.26

x = 0.644 m

Subtracting two to get difference

(0.6526) - (0.644) = 0.0086 cm

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