A uniform horizontal parallel beam of light is incident upon a prism. The prism is the shape of a quarter cylinder of radius=5 and has index of refraction=5/3. The width of the region at which the incident rays after normal incidence on plane surface and subsequent refraction at curved surface intersect on x-axis.





The refractive index of a medium is the ratio of the speed of light in vacuum to the speed of light in the medium.

Refraction of light occurs when it passes from one medium to another with different refractive indices.

The refractive index of the prism is given as 5/3.



The incident ray is a uniform horizontal parallel beam of light.



The prism is in the shape of a quarter cylinder of radius 5.



When the incident ray passes from air to the prism, it undergoes refraction at the plane surface.

The angle of incidence is 0, as the incident ray is parallel to the surface.

The angle of refraction can be found using Snell's Law:

n1 sin θ1 = n2 sin θ2

Here, n1 is the refractive index of air, n2 is the refractive index of the prism, θ1 is the angle of incidence, and θ2 is the angle of refraction.

As the angle of incidence is 0, the angle of refraction is also 0.



When the refracted ray passes from the plane surface to the curved surface of the prism, it undergoes refraction again.

The angle of incidence is 0, as the refracted ray is normal to the plane surface.

The angle of refraction can be found using Snell's Law again:

n1 sin θ1 = n2 sin θ2

Here, n1 is the refractive index of the prism, n2 is the refractive index of air, θ1 is the angle of incidence, and θ2 is the angle of refraction.

As the angle of incidence is 0, the angle of refraction is also 0.



After passing through the prism, the refracted ray is parallel to the incident ray.

The width of the region at which the incident rays after normal incidence on plane surface and subsequent refraction at curved surface intersect on x-axis can be found using the formula:

w = 2r tan⁡(θ/2)

Here, r is the radius of curvature of the curved surface of the prism, and θ is the angle of deviation.

The angle of deviation can be found using the formula:

θ = 2π(n-1)A/λ

Here, n is the refractive index of the prism, A is the angle of the prism, and λ is the wavelength of light.

As the incident ray is a uniform horizontal parallel beam of light, the angle of the prism is 90 degrees.

Substituting the given values, we get:

θ = 2π(5/3-1)(90)/λ

θ = 2π(2/3)(