The index of refraction of silicate flint glass for red light is 1.620 and for violet light is 1.660 . A beam of white light in this glass strikes the glass–air interface at a 23.90° angle of incidence and refracts out into the air. What is the angular separation between the red and violet components of the spectrum that emerges from the glass?

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A1peakenbe A1peakenbe · Answer 1 · 2019-08-08T09:03:10+02:00

Answer:

The angular separation equals [tex]0.35^{o}[/tex]

Explanation:

We have according to Snell's law

[tex]n_{1}sin(\theta _{1})=n_{2}sin(\theta _{2})[/tex]

[tex]\therefore \theta _{2}=sin^{-1}(\frac{n_{1}sin(\theta _{1})}{n_{2}})[/tex]

Using this equation for both the colors separately we have

[tex]\theta _{red}=sin^{-1}(\frac{sin(23.90^{o})}{1.62})\\\\\theta _{red}=14.48^{o}[/tex]

Similarly for violet light we have

[tex]\theta _{violet}=sin^{-1}(\frac{sin(23.90^{o})}{1.660})\\\\\theta _{violet}=14.13^{o}[/tex]

Thus the angular separation becomes

[tex]\Delta \theta =14.48-14.13=0.35^{o}[/tex]

okpalawalter8 okpalawalter8 · Answer 2 · 2022-04-12T14:45:07+02:00

The angular separation between the red and violet components of the spectrum that emerges from the glass is mathematically given as

The difference = 10.16°

Question Parameter(s):

The index of refraction of silicate flint glass for red light is 1.620

and for violet light is 1.660.

the glass-air interface at a 23.90° angle of incidence

Generally, the equation for the Snells Law is mathematically given as

n1sin theta1 = n2sintheta2

Red

(1.620)(sin 25.5) = (1)(sin r)

Angle =35.45°

Violet

(1.660)(sin 25.5) = (1)(sin v)

Angle = 45.6 °

The difference = 45.6- 35.45 = 10.16

The difference = 10.16°

In conclusion, the angular separation between the red and violet components of the spectrum that emerges from the glass is

The difference = 10.16°