water and glass with refractive index of 1.5 are interfaced.if the incident ray are from the water makes an angle 60 degrees with the normal.find the direction of the reflected and refracted rays(given that refractive index of glass to water=1.33)
To find the direction of the reflected and refracted rays at the interface between water and glass, we need to use Snell's law. 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 refractive indices of the two media.
Let's denote:
- Angle of incidence (in water) as θ1 (60 degrees),
- Angle of refraction (in glass) as θ2,
- Refractive index of water as n1 (1.33),
- Refractive index of glass as n2 (1.5).
1. First, we need to find the angle of refraction (θ2) using Snell's law:
n1 * sin(θ1) = n2 * sin(θ2)
Substituting the given values:
1.33 * sin(60 degrees) = 1.5 * sin(θ2)
sin(θ2) = (1.33 * sin(60 degrees)) / 1.5
sin(θ2) ≈ 0.7691
Using the inverse sine (arcsine) function, we find:
θ2 ≈ arcsin(0.7691)
θ2 ≈ 51.49 degrees
2. The direction of the reflected ray can be found using the law of reflection, which states that the angle of incidence is equal to the angle of reflection.
Therefore, the direction of the reflected ray is 60 degrees from the normal, but on the opposite side.
So, the direction of the reflected ray is 60 degrees from the normal, away from the glass.
3. The direction of the refracted ray can be determined using the angles we found:
- The angle of incidence (θ1) is 60 degrees from the normal, towards the glass.
- The angle of refraction (θ2) is 51.49 degrees from the normal, inside the glass.
Therefore, the direction of the refracted ray is 51.49 degrees from the normal, inside the glass.
In summary:
- The direction of the reflected ray is 60 degrees from the normal, away from the glass.
- The direction of the refracted ray is 51.49 degrees from the normal, inside the glass.
To determine the direction of the reflected and refracted rays, we can use the laws of reflection and refraction.
1. Law of Reflection:
When a ray of light is incident on a reflecting surface, the angle of incidence is equal to the angle of reflection, measured with respect to the normal to the surface.
2. Snell's Law of Refraction:
When a ray of light passes from one medium to another, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of velocities of light in the two media.
This is given by: n1 * sinθ1 = n2 * sinθ2
where n1 and n2 are the refractive indices of the initial and final mediums, and θ1 and θ2 are the angles of incidence and refraction respectively.
Now, let's apply these principles to the given scenario:
1. Incident Ray:
The incident ray is coming from water and makes an angle of 60 degrees with the normal. Let's call this angle θ1 = 60 degrees.
2. Refractive Index Calculation:
The refractive index of water to air is approximately 1.33, and the refractive index of glass to air is 1.5.
So, the refractive index of glass to water is:
Refractive Index(glass to water) = Refractive Index(glass to air) / Refractive Index(water to air)
= 1.5 / 1.33
≈ 1.1278
3. Finding the Angle of Refraction:
Using Snell's Law, we can find the angle of refraction (θ2) as follows:
n1 * sinθ1 = n2 * sinθ2
1.5 * sin60° = 1.1278 * sinθ2
0.866 = 1.1278 * sinθ2
sinθ2 = 0.866 / 1.1278
θ2 = arcsin(0.866 / 1.1278)
4. Direction of Reflected Ray:
The angle of reflection (θr) will be equal to the angle of incidence (θ1) with respect to the normal. So, the reflected ray will be perpendicular to the incident ray.
5. Direction of Refracted Ray:
The refracted ray will be bent as it enters the glass due to the change in medium and change in the velocity of light. The direction of the refracted ray will depend on the calculated angle of refraction (θ2) with respect to the normal.
By following these steps and using the given values, we can find the direction of the reflected and refracted rays.