For a glass lens submerged in water (n=1.33), the critical angle of incidence at which total internal reflection begins to happen is 60.1 degrees. What is the index of refraction of the glass?

Question

For a glass lens submerged in water (n=1.33), the critical angle of incidence at which total internal reflection begins to happen is 60.1 degrees. What is the index of refraction of the glass?

Answer 1

sin θ= n(water)/n(glass)

n(glass)= n(water)/ sin θ=1.33/sin60.1=1.53

Answer 2

To find the index of refraction of the glass, we can use Snell's law and the critical angle of incidence.

Snell's law is given by:
n1 sin(θ1) = n2 sin(θ2)

where n1 and n2 are the indices of refraction of the two media, and θ1 and θ2 are the angles of incidence and refraction, respectively.

In this case, the glass is the first medium (n1) and water is the second medium (n2). The critical angle of incidence (θ1c) is the angle at which total internal reflection occurs, meaning that the angle of refraction (θ2c) is 90 degrees.

We can rewrite Snell's law for the critical angle as:
n1 sin(θ1c) = n2 sin(θ2c)
n1 sin(θ1c) = n2 sin(90)

Since sin(90) = 1, the equation becomes:
n1 sin(θ1c) = n2

Substituting the given values:
n1 sin(60.1) = 1.33

We can solve this equation to find the index of refraction (n1):
n1 = 1.33 / sin(60.1)

Using a calculator, we find:
n1 ≈ 1.51

Therefore, the index of refraction of the glass is approximately 1.51.

Answer 3

To find the index of refraction of the glass, we can use Snell's law and the concept of critical angle.

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 indices of refraction:

n1 * sin(theta1) = n2 * sin(theta2)

In this case, n1 is the index of refraction of the air (which is close to 1), n2 is the index of refraction of water (which is given as 1.33), theta1 is the angle of incidence, and theta2 is the angle of refraction.

At the critical angle, the angle of refraction is 90 degrees because the refracted ray is grazing the boundary between the two mediums. Therefore, we can rewrite Snell's law as:

n1 * sin(theta1) = n2 * sin(90)

Since sin(90) = 1, we have:

n1 * sin(theta1) = n2

Now, let's substitute the values we know into the equation. We know that n2 is 1.33 and we are given the critical angle, which is 60.1 degrees.

n1 * sin(60.1) = 1.33

To find n1, we can rearrange the equation:

n1 = 1.33 / sin(60.1)

Using a calculator, we find:

n1 ≈ 1.53

Therefore, the index of refraction of the glass is approximately 1.53.