If the angle of incidence is 30degree and refractive index is 2 find the angle of refraction.find whether the medium is denser or rarer
1*sin30 = 2*sinθ
as for density, review what refractive index means.
To find the angle of refraction, 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 velocities of light in the two mediums. Mathematically, it can be expressed as:
n1 * sin(θ1) = n2 * sin(θ2)
where n1 and n2 are the refractive indices of the two mediums, and θ1 and θ2 are the angles of incidence and refraction, respectively.
In this case, the angle of incidence (θ1) is given as 30 degrees, and the refractive index (n2) is given as 2. We need to find the angle of refraction (θ2).
Let's substitute the given values into Snell's Law:
1 * sin(30) = 2 * sin(θ2)
sin(30) = 2 * sin(θ2)
Now, we can solve for θ2. Divide both sides of the equation by 2:
sin(θ2) = sin(30) / 2
Using a calculator, we find that sin(30) is equal to 0.5, so:
sin(θ2) = 0.5 / 2
sin(θ2) = 0.25
To find θ2, we can use the inverse sine (sin⁻¹) function. Taking the inverse sine of both sides of the equation:
θ2 = sin⁻¹(0.25)
Using a calculator, we find that θ2 is approximately 14.48 degrees.
Now, to determine whether the medium is denser or rarer, we can compare the refractive indices. In this case, the refractive index (n2) is given as 2. Generally, if the refractive index of a medium is higher than that of another medium, it indicates that the medium is denser. Since the refractive index is greater than 1, we can conclude that the medium is denser.