# Prism

Prism is a transparent medium bounded by refracting surfaces such that the incident surface (on which light ray is incidenting) and emergent surface (from which light rays emerges) are plane and non parallel.

# Refraction through a prism

**Fig. 26**

*A*=

*r*

_{1}+

*r*

_{2}and

*i*+

*e*=

*A*+ Î´

For surface ; for surface

*AB*,# Deviation through a prism

For thin prism Î´ = (

*Î¼*â€“ 1)*A*. Also deviation is different for different color light, e.g.,*Î¼*<_{R}*Î¼*, so Î´_{V}_{R}< Î´_{V}.*Î¼*

_{flint}>

*Î¼*

_{Crown}, so Î´

*> Î´*

_{F}

_{C}- Maximum deviation: Condition of maximum deviation is âˆ
*i*= 90Â° â‡’*r*_{1}=*C*,*r*_{2}=*A*â€“*C*and from Snellâ€™s law on emergent surface

**Fig. 27**

- Minimum deviation:
*i*= âˆ*e*and âˆ*r*_{1}= âˆ*r*_{2}=*r*, deviation produced is minimum.

**Fig. 28**

- Refracted ray inside the prism is parallel to the base of the prism for equilateral and isosceles prisms.
- and
- or (Prism formula)

# Condition of no emergence

For no emergence of light, TIR must take place at the second surface

For TIR at second surface,

*r*_{2}>*C*, so,*A*>*r*_{1}+*C*(From*A*=*r*_{1}+*r*_{2})As maximum value of

*r*_{1}=*C,*so,*A*â‰¥ 2*C.*for any angle of incidence.If light ray incident normally on first surface, i.e., âˆ

*i*= 0Â°, it means âˆ*r*_{1}= 0Â°. So in this case condition of no emergence from second surface is*A*>*C*.â‡’ sin

*A*> sin*C*â‡’ sin*A*> 1/*Î¼*â‡’*Î¼*> cosec*A*