for what angle of incidence the lateral shift produced by parallel sided glass plate is (i) zero (ii) maximum
(i) There is no lateral shift for zero degree incidence
(ii) The lateral shift approaches the plate thickness t for angle of incidence of 90 degrees.
For details about case ii, see
http://catarina.udlap.mx/u_dl_a/tales/documentos/lfa/dominguez_r_mz/capitulo3.pdf
90
When the lateral shift is minimum and maximum
To determine the angles of incidence for which the lateral shift produced by a parallel-sided glass plate is zero or maximum, we need to understand the phenomenon of lateral shift and how it relates to the angle of incidence.
When light passes through a parallel-sided glass plate, it undergoes refraction, which causes a change in its direction. This change in direction results in a lateral shift of the light beam. The angle of incidence, which is the angle between the incident ray and the normal to the surface of the glass plate, plays a crucial role in determining the magnitude of the lateral shift.
(i) Zero Lateral Shift:
For a parallel-sided glass plate, there are specific angles of incidence for which the lateral shift is zero. This occurs when the incident ray is parallel to the plane of the glass plate. In this case, the light beam passes through the glass plate without undergoing any deviation or shift. Therefore, the angle of incidence for zero lateral shift is equal to zero degrees.
(ii) Maximum Lateral Shift:
To find the angle of incidence for maximum lateral shift, we can utilize the concept of the critical angle. The critical angle is the angle of incidence at which the refracted ray passes along the interface of the two media, in this case, air and glass. When the angle of incidence is larger than the critical angle, total internal reflection occurs.
In the case of a parallel-sided glass plate, the angle of incidence for maximum lateral shift corresponds to the critical angle. To calculate the critical angle, we first need to know the refractive index of the glass.
Once you know the refractive index of the glass, you can use the formula:
Critical angle = arcsin(1 / refractive index)
The angle of incidence for maximum lateral shift is equal to the critical angle obtained from this formula.
Please note that the refractive index of the glass and the dimensions of the glass plate are essential for calculating the critical angle accurately.