The critical angle at which light will not enter the air from a glass cube with an index of refraction of 1.56 is approximately 39.48 degrees. This is calculated using Snell's Law and represents the angle for total internal reflection.
The minimum angle with the normal inside the glass at which light will not enter the air is known as the critical angle. To calculate this, we use Snell's Law which states n1 sin(θ1) = n2 sin(θ2). For total internal reflection to occur, the angle of refraction θ2 in air (n2 = 1.00) would be 90°, that is the light would travel along the surface.
Setting up the equation for the critical angle θc gives us:
n1 sin(θc) = n2 sin(90°),
where n1 is the index of refraction of glass (1.56) and n2 is the index of refraction of air (1.00). Therefore,
1.56 sin(θc) = 1.00,
This yields:
sin(θc) = 1/1.56,
θc = sin-1(1/1.56),
θc ≈ 39.48°
Therefore, the critical angle is approximately 39.48 degrees. This is the angle at which light striking the surface of the cube inside will undergo total internal reflection, thus not entering the air at this surface.