Two transparent media F and G are separated by a plane boundary. The speed of
light in medium F is 2.0x108 m/sec and in medium G is 2.5x108 m/sec. The critical
angle for which a ray of light from F to G is totally internally reflected is
To find the critical angle for which a ray of light from medium F to medium G is totally internally reflected, we need to use Snell's law and the concept of total internal reflection.
Snell's law relates the angle of incidence (θ₁), the angle of refraction (θ₂), and the refractive indices (n₁ and n₂) of the two media involved. The formula for Snell's law is:
n₁*sin(θ₁) = n₂*sin(θ₂)
In this case, the ray of light is going from medium F to medium G, so we can label them as n₁ and n₂ respectively.
We know the speeds of light in media F and G, but we need to use the refractive indices to find the critical angle. The refractive index (n) of a medium is defined as the ratio of the speed of light in vacuum (c) to the speed of light in that medium (v):
n = c/v
So, we need to find the refractive indices of mediums F and G.
For medium F:
n₁ = c/v₁
n₁ = c/(2.0x10^8 m/sec)
For medium G:
n₂ = c/v₂
n₂ = c/(2.5x10^8 m/sec)
Now we can substitute the refractive indices into Snell's law to find the critical angle.
n₁*sin(θ₁) = n₂*sin(θ₂)
(c/v₁)*sin(θ₁) = (c/v₂)*sin(θ₂)
Simplifying further:
sin(θ₁)/v₁ = sin(θ₂)/v₂
Now, at the critical angle, the angle of refraction (θ₂) is 90 degrees, so sin(θ₂) = 1.
sin(θ₁)/v₁ = 1/v₂
Rearranging, we get:
sin(θ₁) = v₁/v₂
Finally, substitute the values of the speeds of light in media F and G to find sin(θ₁):
sin(θ₁) = (2.0x10^8 m/sec) / (2.5x10^8 m/sec)
Now you can use the inverse sine function (sin⁻¹) to find the value of θ₁, which will give you the critical angle for total internal reflection from medium F to medium G.