Critical Angle of Glass-Air Interface

The critical angle is the angle of incidence at which light is refracted along the interface between two different media. In the case of a glass-air interface, the critical angle determines the maximum angle of incidence at which total internal reflection occurs.

Given:
- Angle of incidence (i) = 45 degrees
- Angle of deviation (d) = 15 degrees

To calculate the critical angle, we can make use of Snell's law, which relates the angle of incidence and angle of refraction to the refractive indices of the two media:

n1 * sin(i) = n2 * sin(r)

Where:
- n1 is the refractive index of the first medium (air)
- n2 is the refractive index of the second medium (glass)
- i is the angle of incidence
- r is the angle of refraction

Step 1: Finding the refractive indices
We need to determine the refractive indices of air and glass. The refractive index of air is approximately 1.00, while the refractive index of glass varies depending on its composition. For simplicity, let's assume the refractive index of glass is 1.50.

Step 2: Calculating the angle of refraction
Using Snell's law, we can rearrange the equation to solve for the angle of refraction:

sin(r) = (n1 * sin(i)) / n2

Plugging in the values, we get:

sin(r) = (1.00 * sin(45°)) / 1.50

sin(r) = 0.7071 / 1.50

sin(r) = 0.4714

Taking the inverse sine of 0.4714, we find:

r ≈ 28.6°

Step 3: Calculating the critical angle
The critical angle occurs when the angle of refraction becomes 90 degrees. At this point, light is refracted along the interface. Therefore, the critical angle can be found by taking the inverse sine of 1 divided by the refractive index of glass:

sin(critical angle) = 1 / n2

sin(critical angle) = 1 / 1.50

sin(critical angle) ≈ 0.6667

Taking the inverse sine of 0.6667, we find:

critical angle ≈ 41.8°

Therefore, the critical angle of the glass-air interface is approximately 41.8 degrees.

Explanation:
When a ray of light is incident on the glass surface at an angle of 45 degrees, it undergoes refraction according to Snell's law. The angle of deviation is given as 15 degrees. By using the refractive indices of air and glass, we can calculate the angle of refraction. Subsequently, the critical angle can be determined by finding the angle at which the refracted ray becomes perpendicular to the interface.