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

Answer:

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

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,

  $1.620 \times \sin 28.30 = 1 \sin \theta _{2}$

Where $\theta _{2} =$ transmitted angle for red light

   $\theta _{2} =$ 50.18°

For violet light,

  $1.660 \times \sin 28.30 = 1 \sin \theta' _{2}$

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°