A certain wave is incident on an interface at an angle of 40 deg. The wave emerges into the other material at an angle of 30 deg. Crossing the interface, the wave:

a. increased speed
b. reduced speed
c. maintained constant

To determine whether the wave increased speed, reduced speed, or maintained a constant speed while crossing the interface, we need to consider the concept of Snell's law.

Snell's law describes the relationship between the angle of incidence (θ1), angle of refraction (θ2), and the refractive indices (n1 and n2) of the two media in contact. It states that:

n1 * sin(θ1) = n2 * sin(θ2)

Where:
- n1 is the refractive index of the incident medium
- n2 is the refractive index of the refracted medium
- θ1 is the angle of incidence
- θ2 is the angle of refraction

In this case, the incident wave is crossing the interface and entering another material. Let's assume the incident medium is medium 1 and the refracted medium is medium 2.

Given:
- Angle of incidence (θ1) = 40°
- Angle of refraction (θ2) = 30°

To determine whether the wave increased speed, reduced speed, or maintained constant speed, we need to compare the refractive indices of the two media.

If the refractive index of medium 2 (n2) is greater than the refractive index of medium 1 (n1), the wave will decrease its speed.

If the refractive index of medium 2 (n2) is less than the refractive index of medium 1 (n1), the wave will increase its speed.

If the refractive indices of both media are equal, the wave will maintain a consistent speed.

To determine the refractive indices, we need to consult the specific values for the materials involved. Refractive indices can vary based on the medium.