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.

θ=arcsin (n2/n1) = arcsin(c•v1/v2•c) = arcsin(2•10⁸/2.5•10⁸) = 45.6°