A) Instead of using a lens with a spherical surface, a lens is formed in the shape of a very shallow cone, a cross section is shown in the diagram below; the cone angle (labelled 0 in the diagram) is 178°. In this example, assume that the incident light is a collimated laser beam of fixed diameter 2d, the refractive index of the optical medium is 1.50 and take the refractive index of air to be 1.00. R d 4/2 e 2L Screen part d Screen part e 1. Sketch a ray diagram to illustrate what happens to the series of rays shown above after transmission through the lens 2. Calculate the angle of incidence of ray R at each refractive surface. 3. Calculate the distance, L, (in terms of distance d) at which ray A crosses the optical axis 4. Sketch the intensity pattern you would expect to see on a screen placed at distance L/2 from the lens 5. Sketch the intensity pattern you would expect to see on a screen at distance 2L from the lens 6. Speculate as to what unusual property the beam from this lens might have; you may wish to think about how the intensity pattern on the screen varies with its distance from the lens and how this would compare to the beam from either a converging or a diverging lens. of

A) Instead of using a lens with a spherical surface, a lens is formed in the shape of a very shallow cone, a cross section is shown in the diagram below; the cone angle (labelled 0 in the diagram) is 178°. In this example, assume that the incident light is a collimated laser beam of fixed diameter 2d, the refractive index of the optical medium is 1.50 and take the refractive index of air to be 1.00. R d 4/2 e 2L Screen part d Screen part e 1. Sketch a ray diagram to illustrate what happens to the series of rays shown above after transmission through the lens 2. Calculate the angle of incidence of ray R at each refractive surface. 3. Calculate the distance, L, (in terms of distance d) at which ray A crosses the optical axis 4. Sketch the intensity pattern you would expect to see on a screen placed at distance L/2 from the lens 5. Sketch the intensity pattern you would expect to see on a screen at distance 2L from the lens 6. Speculate as to what unusual property the beam from this lens might have; you may wish to think about how the intensity pattern on the screen varies with its distance from the lens and how this would compare to the beam from either a converging or a diverging lens. of