a ray enter from denser medium in to air. if angel incident is30 degree and angel of reflection in air 60 degree.find out refractive index of medium ?
sine30*nd=nair*sin60
nd=sin60/sin30=2*sqrt3/2=sqrt3
To find out the refractive index of the medium, you can use Snell's law. Snell's law relates the angles of incidence and refraction to the refractive indices of the two media involved.
Snell's law states:
n1 * sin(theta1) = n2 * sin(theta2)
Where:
- n1 is the refractive index of the initial medium (denser medium)
- theta1 is the angle of incidence
- n2 is the refractive index of the final medium (air)
- theta2 is the angle of refraction
In this case, we are given:
- theta1 (angle of incidence) = 30 degrees
- theta2 (angle of reflection in air) = 60 degrees
First, we need to convert the angles from degrees to radians.
theta1 (in radians) = (30 * pi) / 180
theta2 (in radians) = (60 * pi) / 180
Now we can rearrange Snell's law to solve for n1:
n1 = (n2 * sin(theta2)) / sin(theta1)
We know that n2 is the refractive index of air, which is approximately 1.0003.
Substituting the given values, we get:
n1 = (1.0003 * sin(theta2)) / sin(theta1)
Calculating sin(theta2) and sin(theta1):
sin(theta2) = sin((60 * pi) / 180)
sin(theta1) = sin((30 * pi) / 180)
Now substitute these values back into the equation:
n1 = (1.0003 * sin((60 * pi) / 180)) / sin((30 * pi) / 180)
After evaluating this expression, you will find the refractive index (n1) of the medium from which the ray enters.