A ray of light enters a glass block from air at an angle of incidence of 50 degrees. The angle of refraction is 30 degrees. What is the refractive index of the glass?

What is the value of critical angle for this glass?

Thank you :)

n = sini/sinr =sin 50o/sin 30o =0.766/0.5 = 1.53.

n = sini/sinr =sin 50o/sin 30o =0.766/0.5 = 1.53
α = arcsin (n1/n2) = arcsin (1/1.53) = 40.81o.

To find the refractive index of the glass, we can use Snell's law. Snell's law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the speeds of light in the two media.

1. Start with Snell's law:
n1 * sin(θ1) = n2 * sin(θ2)
Where n1 is the refractive index of the first medium (air), θ1 is the angle of incidence, n2 is the refractive index of the second medium (glass), and θ2 is the angle of refraction.

2. Substitute the given values:
n1 = 1 (refractive index of air)
θ1 = 50 degrees
θ2 = 30 degrees

1 * sin(50) = n2 * sin(30)

3. Solve for n2 by rearranging the equation:
n2 = (sin(50) / sin(30))

Using a calculator, evaluate the expression:
n2 ≈ 1.56

So, the refractive index of the glass is approximately 1.56.

Now, let's find the critical angle for the glass:

The critical angle can be found using the formula:

sin(critical angle) = 1 / refractive index

Substituting the value of the refractive index we found earlier:
sin(critical angle) = 1 / 1.56

Using a calculator, evaluate the expression using inverse sine:
critical angle ≈ 39.2 degrees

So, the value of the critical angle for this glass is approximately 39.2 degrees.

To find the refractive index of the glass and the critical angle, we can use Snell's law:

Snell's law relates the angles of incidence and refraction to the refractive indices of the two materials. It is given by:

n₁ * sin(θ₁) = n₂ * sin(θ₂)

where:
n₁ is the refractive index of the initial medium (in this case, air),
θ₁ is the angle of incidence,
n₂ is the refractive index of the second medium (in this case, glass), and
θ₂ is the angle of refraction.

We are given the angle of incidence (θ₁ = 50°) and the angle of refraction (θ₂ = 30°). We need to find the refractive index of the glass (n₂).

To find n₂, we rearrange Snell's law:

n₂ = (n₁ * sin(θ₁)) / sin(θ₂)

Plugging in the given values, we have:

n₂ = (1 * sin(50°)) / sin(30°)

Using a calculator, we find:

n₂ ≈ 1.7321

So, the refractive index of the glass is approximately 1.7321.

To find the critical angle for this glass, we can use the formula:

sin(θc) = 1 / n

where:
θc is the critical angle, and
n is the refractive index of the glass.

Plugging in the value of the refractive index we found earlier, we have:

sin(θc) = 1 / 1.7321

Using a calculator, we find:

θc ≈ 42.48°

So, the value of the critical angle for this glass is approximately 42.48°.