Introduction:
The critical angle is defined as the angle of incidence in a medium that results in an angle of refraction of 90 degrees in the adjacent medium. It occurs when light is passing from a medium with a higher refractive index to a medium with a lower refractive index. In this case, we have two media, l and ll, with speed of light values of 2 × 10^8 m/s and 2.4 × 10^8 m/s, respectively. We need to calculate the critical angle when light goes from medium l to medium ll.

Refraction and Snell's Law:
When light passes from one medium to another, it changes direction due to the change in speed. This phenomenon is known as refraction. Snell's law relates the angle of incidence (θ1) and angle of refraction (θ2) to the refractive indices (n1 and n2) of the two media:

n1 * sin(θ1) = n2 * sin(θ2)

where n1 and n2 are the refractive indices of the two media.

Critical Angle:
The critical angle occurs when the angle of refraction is 90 degrees. In this case, sin(θ2) becomes 1. We can rearrange Snell's law to solve for the critical angle:

n1 * sin(θ1) = n2 * sin(θ2)
n1 * sin(θ1) = n2 * 1
sin(θ1) = n2 / n1

Taking the inverse sine of both sides:

θ1 = sin^(-1)(n2 / n1)

Calculation:
Given that the speed of light in medium l is 2 × 10^8 m/s and in medium ll is 2.4 × 10^8 m/s, we can calculate the refractive indices using the formula:

Refractive Index (n) = speed of light in vacuum / speed of light in the medium

For medium l:
n1 = 2.998 × 10^8 m/s / 2 × 10^8 m/s = 1.499

For medium ll:
n2 = 2.998 × 10^8 m/s / 2.4 × 10^8 m/s = 1.249

Substituting the values into the formula for the critical angle:

θ1 = sin^(-1)(1.249 / 1.499)

Using a scientific calculator, we can find the inverse sine of (1.249 / 1.499):

θ1 ≈ 48.75 degrees

Critical Angle:
Therefore, the critical angle for light going from medium l to medium ll is approximately 48.75 degrees. This means that if the angle of incidence exceeds 48.75 degrees, total internal reflection will occur, and the light will not be transmitted into medium ll.