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 26.50°. What is the angle of incidence of the violet light?

snells law

sin Incidence= n*sinrefraction

so, then
1= nred/nviolet * sin26.5/sinTheta

To find the angle of incidence of the violet light, we can use Snell's Law, which relates the angle of incidence and angle of refraction of light as it passes through different mediums.

Snell's Law states: n1 * sin(θ1) = n2 * sin(θ2)

Where:
- n1 is the refractive index of the first medium (air in this case)
- θ1 is the angle of incidence of light in the first medium
- n2 is the refractive index of the second medium (crown glass in this case)
- θ2 is the angle of refraction of light in the second medium

We are given the following information:
- For red light: n1 = 1 (refractive index of air), n2 = 1.520 (refractive index of crown glass), and θ1 = 26.50°
- For violet light: n1 = 1 (refractive index of air), n2 = 1.538 (refractive index of crown glass)

Using Snell's Law, we can set up the following equation for red light:

1 * sin(26.50°) = 1.520 * sin(θ2)

Now, let's solve for θ2, the angle of refraction for red light:

sin(θ2) = sin(26.50°) / 1.520
θ2 = arcsin( sin(26.50°) / 1.520 )

After calculating, we find θ2 ≈ 17.089°

Now we can use Snell's Law again to find the angle of incidence for violet light:

1 * sin(θ1_violet) = 1.538 * sin(θ2_violet)

We know that the angle of incidence for both colors is the same, so θ1_violet = θ2_red = 26.50°

Therefore, we can set up the equation as follows:

1 * sin(26.50°) = 1.538 * sin(θ2_violet)

Now, let's solve for θ2_violet, the angle of refraction for violet light:

sin(θ2_violet) = sin(26.50°) / 1.538
θ2_violet = arcsin( sin(26.50°) / 1.538 )

After calculating, we find θ2_violet ≈ 16.371°

Therefore, the angle of incidence of the violet light is approximately 16.371°.