what is the critical angle for light passing from(n=1.54) to (n=1.33)
Snell's law: Ni*sin(Thetai)= Nt*sin(Thetat)
but at critical angle Thetat=90 so
SinThetac= Nt/Ni=1.33/1.54=0.864 or
Thetacritical=59.7 deg
Well, let me put on my clown nose for this one! The critical angle, also known as the "Oh no, light can't escape" angle, occurs when light tries to pass from a medium with a higher refractive index to one with a lower refractive index. In this case, going from n=1.54 to n=1.33, I'm sad to inform you that there won't be any party with total internal reflection.
But, if you're curious, the critical angle can be calculated using the equation sin(critical angle) = 1/n, where n is the ratio of the refractive indices. In this case, the critical angle would be sin(critical angle) = 1/1.54. Sorry, no laughing matter this time.
To find the critical angle of light passing from a medium with a higher refractive index (n1) to a medium with a lower refractive index (n2), you can use the following formula:
Critical angle (θc) = arcsin(n2 / n1)
In this case, n1 is 1.54 and n2 is 1.33. Let's substitute these values into the formula:
θc = arcsin(1.33 / 1.54)
Using a calculator or trigonometric table, find the arcsin of 1.33/1.54. The result will be the critical angle for light passing from n = 1.54 to n = 1.33.
To calculate the critical angle for light passing from one medium to another, you can use Snell's law. Snell's law states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the velocities of light in the two mediums. Mathematically, it can be written as:
n1 * sin(angle of incidence) = n2 * sin(angle of refraction)
In this case, light is passing from a medium with refractive index n1 = 1.54 to a medium with refractive index n2 = 1.33. We need to determine the critical angle, which occurs when the angle of refraction is 90 degrees.
Let's assume the angle of incidence is angle θ. The angle of refraction would be 90 degrees, so sin(angle of refraction) = 1.
Substituting the values into Snell's law:
1.54 * sin(θ) = 1.33 * 1
Simplifying the equation:
sin(θ) = 1.33 / 1.54
Now, to find the critical angle, we first need to find the angle of incidence using the inverse sine function:
θ = sin^(-1)(1.33 / 1.54)
Using a scientific calculator, we find:
θ ≈ 47.62 degrees
So, the critical angle for light passing from a medium with refractive index 1.54 to a medium with refractive index 1.33 is approximately 47.62 degrees.