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A total reflecting prism is a prism made of a high refractive index material such as glass or plastic, with one of the faces coated with a highly reflective material such as aluminum or silver. When light enters the prism, it is totally reflected at the coated face and exits the prism through the other face, without any refraction or transmission.
A right-angled isosceles prism is a prism with a triangular cross-section, where two of the sides are of equal length, and the third side is perpendicular to them. The angles between the sides are 45 degrees and 90 degrees.
A total reflecting prism can be made by using a right-angled isosceles prism and coating the hypotenuse face with a highly reflective material. When light enters the prism at an angle greater than the critical angle, it is totally reflected at the hypotenuse face and exits the prism through the other face, without any loss of energy due to transmission or absorption.
The critical angle is the angle of incidence at which the refracted angle becomes 90 degrees. For a right-angled isosceles prism, the critical angle can be calculated using Snell's law and the geometry of the prism. The critical angle depends on the refractive index of the prism material and the angle of incidence of the light.
Total reflecting prisms have many applications in optics, such as in binoculars, cameras, and laser devices. They are used to direct light without any loss of energy, to change the direction of light, and to create optical illusions.

Right-angled Isosceles Prism
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