To understand why the angle at which the wave must be transmitted in air media is 45 degrees when the angle of reflection is also 45 degrees, we need to consider the laws of reflection and Snell's law.

1. Laws of Reflection:
- The angle of incidence, denoted as θi, is the angle at which the wave strikes the interface between two media.
- The angle of reflection, denoted as θr, is the angle at which the wave is reflected off the interface.
- According to the laws of reflection, the angle of incidence is equal to the angle of reflection: θi = θr.

2. Snell's Law:
- Snell's law relates the angles of incidence and transmission to the refractive indices of the two media.
- It states that the ratio of the sine of the angle of incidence to the sine of the angle of transmission is equal to the ratio of the refractive indices of the two media: sin(θi) / sin(θt) = n1 / n2.

In this case, we have an air medium (n1) and another medium (n2) from which the wave is being reflected. We are given that the angle of reflection (θr) is 45 degrees. We need to find the angle of transmission (θt).

To solve this problem, we can use Snell's law and the fact that the angle of incidence (θi) is equal to the angle of reflection (θr).

- According to the laws of reflection, θi = θr = 45 degrees.
- Let's assume that the angle of transmission is θt.
- We know that the refractive index of air (n1) is approximately 1, as air is considered to be a vacuum for most practical purposes.
- Using Snell's law, we have sin(θi) / sin(θt) = n1 / n2 = 1 / n2.

Now, substituting the values into Snell's law equation:

sin(45) / sin(θt) = 1 / n2

Since sin(45) is equal to √2 / 2, the equation becomes:

√2 / 2 / sin(θt) = 1 / n2

Cross-multiplying, we get:

√2 / 2 = sin(θt) / n2

Rearranging the equation:

sin(θt) = (√2 / 2) * n2

To find the angle of transmission, we take the inverse sine of both sides:

θt = sin^(-1)((√2 / 2) * n2)

Since the refractive index of air (n1) is approximately 1, the equation simplifies to:

θt = sin^(-1)(√2 / 2)

Evaluating this expression, we find that θt is approximately 45 degrees.

Therefore, the angle at which the wave must be transmitted in air media when the angle of reflection is 45 degrees is 45 degrees.