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 1.78 cm thick, and then back to air.

(a) If the beam has an angle of incidence of 30.6° 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

(a) Angle of Emergence :

Applying Snell's law

For red,

n1sini=n2sinr ................. (1)

Where,

n1 = refractive index in air=1

n2 = refractive index in glass fr red light= 1.512

i = angle of incidence= 30.6°

r= angle of emergence

Putting all the values in equation (1)

We get,

r= 19.6739° for red

now for violet,

Applying snell's law,

n2sini= n3sinr ................(2)

Where, n1= refractive index in glass for violet= 1.53

n2= refractive index in air= 1

i= angle of incidence = 19.67°

r= angle of refraction

Putting all the values in equation (2)

We get,

r=30.9975° for violet

(b) Distance separating lights :

we know that,

optical path of light= ( n2 - n1) x t

where,

n1= 1.530

n2=1.512

t= thickness of the glas = 1.78 cm

putting all the values in equation (3)

we get,

distance separating the lights= 0.03204 cm

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