Question

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 28.30 ∘ 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?

Answer 1

The angular separation between the red and violet components of the spectrum that emerges from the glass is 1.72°

Step-by-step explanation:

Given:

Refractive index for red light
`n _(1) = 1.620`

Refractive index for violet
`n' _(1) = 1.660`

Refractive index for air
`n_(2) = 1`

Incident angle
`\theta _(1) =` 28.30°

According to the snell's law,

`n_(1) \sin \theta _(1) = n_(2) \sin \theta _(2)`

For red light,

`1.620 * \sin 28.30 = 1 \sin \theta _(2)`

Where
`\theta _(2) =` transmitted angle for red light

`\theta _(2) =` 50.18°

For violet light,

`1.660 * \sin 28.30 = 1 \sin \theta' _(2)`

Where
`\theta' _(2) =` transmitted angle for violet light

`\theta' _(2) =` 51.9°

Angular separation between red and violet light is given by,

`\theta ' _(2) - \theta _(2) = 51.9 -50.18 =` 1.72°

Therefore, the angular separation between the red and violet components of the spectrum that emerges from the glass is 1.72°