For a prism, when the light undergoes minimum deviation, the relationship between the angle of incidence ($i$)

Question

For a prism, when the light undergoes minimum deviation, the relationship between the angle of incidence ($i$) and the angle of emergence ($i'$) is:

Accepted Answer

1. **Prism Deviation:** When a ray of light passes through a prism, the angle of deviation $\delta$ depends on the angle of incidence $i$. 
2. **Condition for Minimum Deviation:** As the angle of incidence increases, the angle of deviation first decreases, reaches a minimum value (called the angle of minimum deviation, denoted by $\delta_m$), and then increases. 
3. **Symmetry at Minimum Deviation:** At the specific position of minimum deviation ($\delta = \delta_m$), the light ray passes symmetrically through the prism. 
4. **Conclusion:** Because of this symmetrical passage, the angle of incidence becomes exactly equal to the angle of emergence ($i = i'$ or $i = e$). Additionally, the angles of refraction at the two faces are equal ($r_1 = r_2$), and the refracted ray inside the prism is parallel to its base.

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