Question

Under what condition is the deviation caused by a prism directly proportional to its refractive index?​

Answer 1

Answer:

In a prism, the angle of deviation({\displaystyle \delta } \delta) decreases with increase in the angle of incidence({\displaystyle i}i) up to a particular angle. This angle of incidence where the angle of deviation in a prism is minimum is called the Minimum Deviation Position of the prism and that very deviation angle is known as the Minimum Angle of Deviation (denoted by {\displaystyle \delta _{min}}{\displaystyle \delta _{min}}, {\displaystyle D_{\lambda }}{\displaystyle D_{\lambda }} or {\displaystyle D_{m}}{\displaystyle D_{m}}).

Explanation:

In a prism, the angle of deviation({\displaystyle \delta } \delta) decreases with increase in the angle of incidence({\displaystyle i}i) up to a particular angle. This angle of incidence where the angle of deviation in a prism is minimum is called the Minimum Deviation Position of the prism and that very deviation angle is known as the Minimum Angle of Deviation (denoted by {\displaystyle \delta _{min}}{\displaystyle \delta _{min}}, {\displaystyle D_{\lambda }}{\displaystyle D_{\lambda }} or {\displaystyle D_{m}}{\displaystyle D_{m}}).

In Minimum Deviation, the refracted ray in the prism is parallel to its base. In other words, the light ray is symmetrical about the axis of symmetry of the prism.[1][2][3] Also, the angles of refractions are equal i.e. {\displaystyle r_{1}=r_{2}}{\displaystyle r_{1}=r_{2}}. And, the angle of incidence and angle of emergence equal each other ({\displaystyle i=e}{\displaystyle i=e}). This is clearly visible in the graph in the next section