When light enters a medium with a different refractive index, it generally undergoes refraction, which is the bending of light due to the change in its speed. However, in the specific case you described, where light is shined at the center of the straight side of a semi-circular glass block, there is no refraction observed when the light enters the glass block through the curved side. This phenomenon is known as the "critical angle" or "total internal reflection."
To understand why total internal reflection occurs in this case, we need to consider the principles of refraction and the critical angle. When light passes from one medium to another with a different refractive index, it bends according to Snell's law, which 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 refractive indices of the two media.
However, when the angle of incidence exceeds a certain critical angle, which depends on the refractive indices of the two media, the light is no longer refracted. Instead, it undergoes total internal reflection, meaning it is completely reflected back into the original medium.
In the case of the semi-circular glass block, the light is entering from air (which has a lower refractive index) to glass (which has a higher refractive index). When the light is incident at the center of the straight side, it is perpendicular to the surface and is therefore not refracted. As it reaches the curved side of the glass block, it encounters the boundary between the glass and air at an angle of 90 degrees with respect to the normal. Since this angle of incidence is larger than the critical angle for the glass-air interface, total internal reflection occurs, and the light is reflected back into the air.
So, in summary, the light does not refract at the curved side of the glass block because it is incident at a critical angle that causes total internal reflection to occur.