A Ray of light in ait strikes a plane surface of a crown glass block at an angle of 50 degrees to the normal.
In what direction does the Ray travel through the glass block .
(Refractive index of glass=1.5)
What is the maximum angle of incidence for a Ray travelling from the glass block into air if the Ray is to Refractive out of the block.
To determine the direction in which the ray of light travels through the glass block, we need to apply the laws of refraction. The first law of refraction, also known as Snell's law, states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the speeds of light in the two mediums. Mathematically, this can be written as:
sin(angle of incidence) / sin(angle of refraction) = speed of light in first medium / speed of light in second medium
In this case, the first medium is air and the second medium is the crown glass block.
Given:
Angle of incidence (θ₁) = 50 degrees
Refractive index of glass (n) = 1.5
To find the angle of refraction (θ₂), we can rearrange Snell's law and solve for sin(θ₂):
sin(θ₂) = (sin(θ₁) * speed of light in first medium) / speed of light in second medium
Since the speed of light in a vacuum is the same as in air, we can simplify this to:
sin(θ₂) = sin(θ₁) / n
Now we can substitute the values and calculate:
sin(θ₂) = sin(50) / 1.5 ≈ 0.572061
θ₂ ≈ arcsin(0.572061) ≈ 34.44 degrees
Therefore, the ray of light refracts and travels through the glass block at an angle of approximately 34.44 degrees to the normal.
Now let's move on to the second part of the question, which asks for the maximum angle of incidence for a ray traveling from the glass block into air in order to refract out of the block.
According to Snell's law, when light travels from a denser medium (glass block) to a rarer medium (air), the refracted ray bends away from the normal. At a certain critical angle, the refracted angle would become 90 degrees, and the light would no longer refract but undergo total internal reflection.
To find the maximum angle of incidence (θc), we use the formula:
sin(θc) = 1 / n
Substituting the refractive index of glass (n = 1.5), we have:
sin(θc) = 1 / 1.5 ≈ 0.66667
θc ≈ arcsin(0.66667) ≈ 42.72 degrees
Therefore, the maximum angle of incidence for a ray traveling from the glass block into air, in order to refract out of the block, is approximately 42.72 degrees.
I hope this explanation helps! Let me know if you have any further questions.