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 2.48 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)

red=____degrees

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?°

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

** I got 15.86 degrees for RED and 15. 66 for VIOLET but they were both wrong.

I'm not sure what I'm doing wrong, Please help. THANK YOU!!

red=____degrees

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

(a) Since angle of emergence= angle of incidence, both lights emerge at 24.4o

(b) When red and violet light emerges from glass, they form a parallel beam. To find distance between them, we will first find the angle of refraction for these lights when they strike air-glass interface

Red light:

n1 sin i = n2 sin r

(1) sin 24.4 = 1.512 sin r

r = 15.8558o

For violet:

n1 sin i = n2 sin r'

(1) sin 24.4 = 1.530 sin r'

r' = 15.6644o

Red light strikes other end of glass slab at x = 2.48 tan 15.8558o = 0.70438 cm

Violet light strikes other end of glass slab at x' = 2.48 tan 15.6644o = 0.69543cm

Difference = x - x' = 8.9 x 10^-3 cm

Distance separating the red and violet light as it emerges from the glass = (x-x') cos 24.4 = 8.1468 x 10^-3 cm

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