The refractive index of any medium with respect to air is √2 ,the angle of incidence is 45 degree. Find out the angle of refraction and angle of deviation.
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The refractive index of any medium with respect to air is √2 ,the angle of incidence is 45 degree. Find out the angle of refraction and angle of deviation.
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Answer:
Explanation:To find the angle of refraction and angle of deviation, we can use Snell's Law, which relates the angle of incidence (i), the angle of refraction (r), and the refractive indices of the two media. Snell's Law is given by:
n1 * sin(i) = n2 * sin(r)
In this case, n1 is the refractive index of air (which is approximately 1), and n2 is the refractive index of the medium. Given that the refractive index of the medium with respect to air is √2, n2 = √2.
We are given that the angle of incidence (i) is 45 degrees. We can now use Snell's Law to calculate the angle of refraction (r):
1 * sin(45 degrees) = √2 * sin(r)
sin(45 degrees) = √2/2
Now, let's solve for sin(r):
sin(r) = (√2/2) / √2
sin(r) = 1/2
Now, we can find the angle of refraction (r) by taking the arcsine (inverse sine) of 1/2:
r = arcsin(1/2)
r ≈ 30 degrees
So, the angle of refraction is approximately 30 degrees.
To find the angle of deviation (D), you can use the formula for the angle of deviation:
D = i - r
D = 45 degrees - 30 degrees
D = 15 degrees
The angle of deviation is 15 degrees.
[tex]\bf{Answer:}[/tex]
To find the angle of refraction and angle of deviation, we can use Snell's Law, which relates the angles of incidence and refraction to the refractive indices of the two mediums:
Snell's Law: n1 * sin(θ1) = n2 * sin(θ2)
Here, n1 is the refractive index of the first medium (air), n2 is the refractive index of the second medium, θ1 is the angle of incidence, and θ2 is the angle of refraction.
Given:
n1 (refractive index of air) = 1 (approximately)
n2 = √2
θ1 (angle of incidence) = 45 degrees
We want to find θ2 (angle of refraction).
Let's rearrange Snell's Law to solve for θ2:
sin(θ2) = (n1 / n2) * sin(θ1)
sin(θ2) = (1 / √2) * sin(45 degrees)
sin(θ2) = (1 / √2) * (1 / √2) (sin(45 degrees) = 1 / √2)
sin(θ2) = 1/2
Now, to find θ2, take the arcsin (inverse sine) of 1/2:
θ2 = arcsin(1/2)
θ2 ≈ 30 degrees
So, the angle of refraction (θ2) is approximately 30 degrees.
To find the angle of deviation, you would need more information about the geometry of the situation, such as the shape of the boundary between the two mediums (e.g., flat surface, prism, etc.). The angle of deviation depends on the specific conditions and geometry of the problem.