Red light (n = 1.520) and violet light (n = 1.538) traveling in air are incident on a slab of crown glass. Both colors enter the glass at the same angle of refraction. The red light has an angle of incidence of 20.97°. What is the angle of incidence of the violet light? Give your answer to four significant figures.

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n₁ = 1.520

n₂= 1.538
n₁=sini₁/sinr₁
n₂=sini₂/sinr₂
sinr₁=sinr₂
sini₁/n₁=sini₂/n₂
sini₂=n₂•sini₁/n₁=1.538•sin 20.97/1.52 =0.3621
i₂=21.23°

To solve this problem, we need to use Snell's Law, which relates the angles of incidence and refraction of light passing through different mediums.

Snell's Law is given by:
n₁sin(θ₁) = n₂sin(θ₂)

Where:
n₁ = refractive index of the first medium (air)
n₂ = refractive index of the second medium (crown glass)
θ₁ = angle of incidence of the first light
θ₂ = angle of incidence of the second light

For the red light:
n₁ = 1 (since it is traveling in air)
n₂ = 1.520 (given refractive index of crown glass)
θ₁ = 20.97° (given angle of incidence of red light)

We can rearrange Snell's Law to solve for θ₂:
sin(θ₂) = (n₁ / n₂) * sin(θ₁)

Plugging in the values:
sin(θ₂) = (1 / 1.520) * sin(20.97°)

Using your calculator or a trigonometric table, calculate the value of sin(θ₂). Let's assume it is equal to x.

Now, to find the angle of incidence of the violet light, we need to find the inverse sine of x:
θ₂ = arcsin(x)

Calculate the inverse sine of x using your calculator or computer software. Round the result to four significant figures.

This will give you the angle of incidence of the violet light.