Geometric Optics 1

There are no complicated calculations involved. In fact, you don't even have to evaluate any trigonometric expressions.

Consider the total horizontal distance traveled. To reach point $B,$ the ray must travel half the square's length, then the entirety of the square's length; this is equal to $\frac{3}{2}\times L.$

Now consider the vertical distance traveled. The ray must travel the square's length twice: this is equal to $2\times L.$

The cotangent is defined as the quotient of the adjacent leg to the opposite leg, and since we are measuring the angle with respect to the horizontal, $\cot(\alpha) = \frac{\text{horizontal distance}}{\text{vertical distance}}$ $\cot(\alpha) = \frac{(3/2) L}{2 L} = \boxed{\frac{3}{4}}$