A light Ray is incident at an angle of 45 degrees on one side of a glass plate of index of refraction 1.6. Find the angle at which the ray emerges from the other side of the plate
26.22
To find the angle at which the light ray emerges from the other side of the glass plate, we 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 indices of refraction:
n1 * sin(θ1) = n2 * sin(θ2)
Where,
n1 is the index of refraction of the medium the light ray is coming from,
θ1 is the angle of incidence,
n2 is the index of refraction of the medium the light ray is entering into, and
θ2 is the angle of refraction.
In this case, the angle of incidence is 45 degrees and the index of refraction of the glass plate is 1.6.
Let's calculate the angle at which the ray emerges from the other side of the plate:
n1 = air (index of refraction of air) = 1 (approximate value)
θ1 = 45 degrees
n2 = 1.6 (index of refraction of glass plate)
Using Snell's law, we can determine θ2:
1 * sin(45) = 1.6 * sin(θ2)
Rearranging the equation, we have:
sin(θ2) = (1 * sin(45)) / 1.6
sin(θ2) = 0.707 / 1.6
Taking the inverse sine on both sides of the equation, we get:
θ2 = sin^(-1)(0.707 / 1.6)
Using a calculator, we find:
θ2 ≈ 26.5 degrees
Therefore, the light ray emerges from the other side of the glass plate at an angle of approximately 26.5 degrees.
To find the angle at which the light ray emerges from the other side of the glass plate, we can use Snell's Law which 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 indices of refraction of the two media involved.
Mathematically, Snell's Law can be expressed as:
n1 * sin(theta1) = n2 * sin(theta2)
Where:
n1 is the refractive index of the first medium (in this case, air), which is approximately 1.0.
theta1 is the angle of incidence, which is given as 45 degrees.
n2 is the refractive index of the second medium (in this case, glass), which is given as 1.6.
theta2 is the angle of refraction, which we need to find.
Using the equations above, we can rearrange Snell's Law to solve for theta2:
sin(theta2) = (n1 * sin(theta1)) / n2
Now let's substitute the given values into the equation:
sin(theta2) = (1.0 * sin(45 degrees)) / 1.6
Calculating sin(45 degrees) gives us approximately 0.7071, so the equation becomes:
sin(theta2) = (1.0 * 0.7071) / 1.6
Dividing the numerator by the denominator, we get:
sin(theta2) = 0.4407
To find theta2, we can use the inverse sine function (also known as arcsin). Taking arcsin of both sides gives us:
theta2 = arcsin(0.4407)
Using a scientific calculator, we find that theta2 is approximately 26.7 degrees.
Therefore, the light ray emerges from the other side of the glass plate at an angle of approximately 26.7 degrees.