Final answer:
To calculate the critical angle for an optical fiber with a core refractive index of 1.4 and a relative refractive index of 2.5%, first find the cladding's refractive index, then use Snell's law to find the critical angle by taking the inverse sine of the ratio of the cladding's to the core's refractive index.
Step-by-step explanation:
The question asks us to determine the critical angle for an optical fiber with a core refractive index of 1.4 and a relative refractive index of 2.5%. The relative refractive index is the percentage difference between the refractive index of the core and the cladding of the fiber.
To find the refractive index of the cladding (n2), we use the given relative refractive index percentage:
1.4 - (1.4 * 2.5/100) = 1.4 - 0.035 = 1.365.
The formula to calculate the critical angle (c) when light is passing from a denser medium to a less dense medium (from the core to the cladding of the optical fiber) is given by Snell's law for total internal reflection:
c = sin-1(n2/n1),
where n1 is the refractive index of the core (1.4) and n2 is the refractive index of the cladding (1.365).
Applying the values to the formula, we get:
c = sin-1(1.365/1.4).
To find the critical angle, calculate the inverse sine (sin-1) of the ratio 1.365/1.4, which gives us the critical angle for the optical fiber.