Question bank: Geometric Optics: Parallel Plates

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.

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.

A glass blade with an absolute refractive index of 1.5 is immersed in air and positioned in such a way that light strikes the blade at an angle of 60 degrees to the normal. The blade is so thin that it can be considered as two parallel flat surfaces. The light incident on the blade undergoes refraction twice, once at the entrance and once at the exit, causing a noticeable lateral displacement. Considering Snell's law and that sin(60 degrees) = square root of 3/2, calculate the lateral displacement suffered by the light when crossing the glass blade. Consider that the blade has a thickness of 1 mm and that the light beam strikes perpendicularly to the first surface of the blade. For your answer, you may need concepts of trigonometry and calculation of sines and cosines, as well as the application of Snell's law twice for the two refractions that occur.

A Physics student wants to investigate the effect of parallel blades on the refraction and linear deviation of light. He uses a glass blade with parallel faces and a refractive index n = 1.5, with a monochromatic light beam incident at an angle of 30° relative to the normal. (a) Determine the angle of refraction of the light beam upon entering the glass blade and calculate the angle of incidence and emergence of the light beam upon exiting the glass blade. (b) Find the linear deviation that occurs to the light beam due to the presence of the glass blade, assuming the thickness of the blade is 3 cm. (c) Explain how the linear deviation found in this experiment can be applied in everyday situations, such as the use of lenses and optical systems.