Question bank: Geometric Optics: Parallel Plates

During a Physics class on the phenomenon of light refraction, a teacher proposed an experiment to the students involving the immersion of a rectangular glass blade in the air and later in a liquid with a known refractive index. The blade was then observed laterally, and the class was challenged to determine the lateral displacement of the image observed through the blade. Knowing that the refractive index of the glass is n_v = 1.50 and that the blade has a thickness of d = 1.00 cm, the students planned the experiment and measured the image deviation, obtaining a value of 0.60 cm. Based on this information, and considering the experimental situation described, what is the refractive index of the liquid in which the glass blade was immersed? Additionally, discuss how the variation of the lateral displacement of the image would be related to a change in the inclination of the blade in relation to the direction of the incident light.

In a laboratory experiment, a monochromatic light beam is incident perpendicularly on a glass plate with parallel faces. Then, the plate is removed and replaced by a plate of a different material, with the same thickness but a different refractive index from the glass. When observing the emerging beam, a lateral displacement of the beam is observed. Knowing that the refractive index of the glass is 1.50 and that the observed lateral displacement is 6.0 cm, determine the refractive index of the new material. Consider that the plate is very thin compared to the other dimensions involved in the experiment, and disregard light absorption effects.

Explain, from a scientific perspective, how linear deviation occurs in parallel plates and how Snell's law can be used to calculate this deviation. Give a practical example to illustrate the application of Snell's law in this context.

When crossing a glass plate with a thickness of 4.0 cm and a refractive index of 1.5, a light beam undergoes a lateral displacement of 1.0 cm. Considering the small angles approximation and that the glass blade is much larger compared to the lateral displacement, calculate the angle of incidence of the light beam on the first surface of the glass plate. Use Snell's law for refraction and assume that the external medium is air with an index of refraction approximately equal to 1.

For a Science Museum project, a group of high school students wants to create an experience that demonstrates the phenomenon of lateral deviation of light when passing through parallel slabs. They plan to use a rectangular block of transparent and homogeneous material, with a known refractive index. The structure will have the shape exemplified in the figure below, with a cross-sectional width of 10 cm and an unknown height. When a beam of light is incident parallel to the base of the block, the goal is to calculate the height h of the slab, so that the lateral displacement of light is 1.5 cm when it emerges from the block, knowing that the refractive index of the material is 1.5. Considering that light passes from a medium with a refractive index of n1 to a medium with a refractive index of n2, where n2 > n1, and that the slab is much thicker than the wavelength of light, what is the height h of the rectangular block?