A ray of red light, for which n=1.54, and a ray of violet light, for which n=1.59, travel through a piece of glass. They meet right at the boundary between the glass and the air, and emerge into the air as one ray with an angle of refraction of 22.5.

What is the angle between the two rays in the glass?

Use Snell's law to find each incident angle, then take the difference.

Nair*sinIncidence=Nglass*SinRefracted.
find each angle of incidence withthat.

To determine the angle between the two rays in the glass, we can use Snell's Law, which states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the refractive indices of the two media:

n₁ * sin(θ₁) = n₂ * sin(θ₂)

Where:
- n₁ and n₂ are the refractive indices of the two media
- θ₁ is the angle of incidence
- θ₂ is the angle of refraction

We are given the refractive indices:
- n₁ (red light) = 1.54
- n₂ (violet light) = 1.59

Let's assume that the angle between the two rays in the glass is θ. Since the two rays meet at the boundary between the glass and air, their angles of incidence and refraction will be the same.

Using Snell's Law for the red light:
1.54 * sin(θ) = 1 * sin(22.5) (Note: sin(θ₁) = sin(θ₂) = sin(θ) in this case, as the two rays meet at the boundary)

Now let's solve for sin(θ):
sin(θ) = (1 * sin(22.5)) / 1.54

Similarly, using Snell's Law for the violet light:
1.59 * sin(θ) = 1 * sin(22.5)

Now let's solve for sin(θ):
sin(θ) = (1 * sin(22.5)) / 1.59

By comparing the two equations, we can see that sin(θ) is the same for both the red and violet light rays in the glass. Therefore, the angle between the two rays in the glass, denoted as θ, is the same for both rays.

Hence, to find θ, we can use either equation with the given values:

sin(θ) = (1 * sin(22.5)) / 1.59

Now, we can take the inverse sine (sin⁻¹) of both sides to find θ:

θ ≈ sin⁻¹((1 * sin(22.5)) / 1.59)

Evaluating this expression will give us the approximate value of θ, which represents the angle between the two rays in the glass.