Explanation:
When a ray of light passes from one medium to another, it bends or changes its direction. This phenomenon is called refraction. The bending of light depends on the refractive indices of the two media and the angle of incidence of the light ray.

The angle of incidence is the angle between the incident ray and the normal, which is a line perpendicular to the surface of the medium. The angle of refraction is the angle between the refracted ray and the normal.

Formula:
The relationship between the angle of incidence and the angle of refraction is given by Snell's law, which states that:

n1*sin(i) = n2*sin(r)

Where n1 and n2 are the refractive indices of the two media, i is the angle of incidence, and r is the angle of refraction.

Given:
In this question, we are given that the angle of refraction is half of the angle of incidence. Let us assume that the angle of incidence is 'x'. Then, the angle of refraction would be 'x/2'.

Solution:
Using Snell's law, we can write:

n1*sin(x) = n2*sin(x/2)

Dividing both sides by sin(x), we get:

n1/n2 = sin(x/2)/sin(x)

Now, we know that the refractive index of a medium is always greater than or equal to 1. Therefore, we can say that:

sin(x/2)/sin(x) <=>

Dividing both sides by sin(x/2), we get:

1/sin(x) >= 2/sin(x/2)

Using the trigonometric identity, sin(2x) = 2*sin(x)*cos(x), we can write:

1/sin(x) >= sin(x)/cos(x)

Multiplying both sides by sin(x)*cos(x), we get:

cos(x) >= sin^2(x)

Using the trigonometric identity, sin^2(x) + cos^2(x) = 1, we can write:

cos(x) >= 1 - cos^2(x)

Simplifying further, we get:

cos^2(x) + cos(x) - 1 <=>

Using the quadratic formula, we can solve for cos(x):

cos(x) = [-1 ± sqrt(5)]/2

Now, we know that the angle of incidence cannot be negative. Therefore, we can ignore the negative solution and take the positive one:

cos(x) = [-1 + sqrt(5)]/2

Using the inverse cosine function, we can find the value of x:

x = cos^-1{[-1 + sqrt(5)]/2}

x = 48.19 degrees (approx.)

Therefore, the angle of incidence is approximately 48.19 degrees.

Answer:
The angle of incidence is approximately 48.19 degrees.