The critical angle between an equilateral prism and air is 45 degrees.if the incident ray is perpendicular to the refracting surface,then what happens?
It is totally reflected from the second surface and emerges out perpendicularly from third face into air
So,in the question it is given angle od incidence is 90 degree.(perpendicular to refracting surface ).Now since it is an equateral triangle each angle is 60 degree.As the light touches the 2 nd surface we can see a triangle there with angles 60 degree and 90 degree so obviously the other angle is 30 degree.when we draw a normal we can understand that angle of incidence is 60 degree (90-30) .Given critical angle is 45 degree.here angle of incidence is greater than 45 i.e, 60 degree.so this is the condition for TIR.so it will get reflected to the same medium.Again when the light ray reaches the 3 rd side we can again consider a triangle . calculating the angles we will get angle of refraction ad 90 degree. so it will emerge out perpendicular to the 3 rd surface.
Hope this helps.😊
nothing.
If the critical angle between an equilateral prism and air is 45 degrees, it means that any incident ray that strikes the refracting surface of the prism at an angle greater than 45 degrees will be completely internally reflected. In other words, the light will not pass through the prism and will bounce back into the air.
Now, you mentioned that the incident ray is perpendicular to the refracting surface. If the incident ray is perpendicular, it means that the angle of incidence is 0 degrees (since the angle between a perpendicular line and any other line is always 90 degrees and the angle of incidence is the angle between the incident ray and the normal to the surface, which is always perpendicular). Since the angle of incidence is less than the critical angle of 45 degrees, the incident ray will not be completely internally reflected. Instead, it will pass through the prism, potentially undergoing refraction as it enters and exits the prism.
To further understand what happens to the ray, you can 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:
n₁sin(θ₁) = n₂sin(θ₂)
Where:
- n₁ is the refractive index of the medium the ray is coming from (in this case, air)
- θ₁ is the angle of incidence
- n₂ is the refractive index of the medium the ray is entering (in this case, the prism)
- θ₂ is the angle of refraction
If the incident ray is perpendicular to the refracting surface (θ₁ = 0), then sin(θ₁) = sin(0) = 0. As a result, the left side of the equation becomes 0. Therefore, the angle of refraction (θ₂) can be any value, as long as it satisfies Snell's law. This means that the ray can exit the prism at any angle, depending on other factors such as the refractive index of the prism material.
In summary, if the incident ray is perpendicular to the refracting surface of an equilateral prism and the critical angle is 45 degrees, the ray will not be internally reflected and will pass through the prism, potentially undergoing refraction. The exact angle of refraction will depend on the refractive index of the prism material.