Question

A glass prism is able to produce spectrum when white light passes through it but a glass slab doesn't produce any spectrum

Answer 1

Hi there !!

A glass prism is able to produce a spectrum , which is a patch of light obtained due to dispersion. This is because the opposite refracting faces of a glass prism are not parellal. Thus, the incident ray is not parellal to the emergent ray and is deviated by the angle of deviation.
A glass slab is a rectangular structure in which the opposite refracting faces are parellal to each other. The result is that , the emergent is parellal to the incident ray but is literally displaced from it.
Thus, a rectangular glass slab is unable to produce a spectrum due to the refracting faces being parellal to each other .

Answer 2

In the case of a glass slab, the two interfaces the light ray has to pass are parallel to each other. In this case the emergent ray is also a white light because the constituents of whitelight which are refracted at different angles at the first interface recombine at the second interface and emerge as a sigle white light. In the case of a prism, the two interfaces the light ray has to pass are not parallel to each each other and are inclined at an angle. In this case, the effects of the first interface are not reversed and the colors separated at that first interface continue along different paths upon leaving the glass at the second interface. Hence we observe a spectrum on the other sisde.