Question

Show that the limiting value of the angle of prism is twice its critical angle?

Answer 1

Angle of prism is the angle between the two surfaces of the prism from which the light ray enters inside the prism and from the light ray goes out after refraction. An optical prism is a transparent material optical element with flat, polished 5 surfaces that refract light. At least one surface has to be angled—elements with parallel surfaces are not prisms.

Step by step answer:
The conventional geometrical form of an optical prism is that of a triangular prism with a triangular base and square sides, and in colloquial use "prism" commonly refers to this type. Some kinds of optical prisms aren't in truth inside the form of geometric prisms. Prisms may be crafted from any fabric this is transparent to the wavelengths for which they're designed. Typical substances include glass, plastic, and fluorite, etc.
Angle of prism= $A = {r_1} + {r_2}$
in a case with the triangular prism where ${i_1} = {i_2} = 90^\circ$
than ${r_1} = {r_2} = c$
c = critical angles
so, $A = c + c$
$A = 2c$

Dispersive prisms are used to interrupt up light into its spectral colouring due to the fact the refractive index relies upon frequency; the white light coming into the prism is a combination of various frequencies and visible different colours , every of which receives bent slightly differently.
So, the limiting value of the Angle of prism is twice that of its critical angle.

Note: while the critical angle is defined as the angle of refraction when a ray of light enters from on side and refracts and comes out from the other side of the prism.