Saved Bookmarks
| 1. |
Derive n= (sin""(A+D)/(2))/( sin ""(A)/(2)) for the prism. Where the symbols have their usual meaning. |
Answer» SOLUTION :Consider a principal section of prism of reflecting angle A and refractive index n placed in a air MEDIUM. A ray of light PQ is incident on the face AB refraction takes place and finally EMERGES out with an angle `i_2`,  fromthe quadrilateralAQXR ` A +ANGLEX = 180 ^@` `A = 180- angleX ` fromthe triangle`QX R` ` r_1 +r_2= 180- angleX --- (2)` from(1)& (2) `A=r_1+r_2 ---(3)` fromfigure ` delta= i_1 -r_1+i_2-r_2` ` delta =i_1+i_2 -(r_1 +r_2)` `delta =i_1 +i_2-A ---(4)` As the angle of incidence increases, since deviation decreases and reaches a minimum then after it increases as angle incidence increases. At minimum deviation position. if ` delta =D ` ` i_1 =i_2 =i` eqn (3)& (4)becomes `A =r +r impliesA=2r` `implies r =(A)/(2)` ` D=i +i -A implies i =(A +D )/(2 )` from snells law `n = ( sin i)/( sin r)` ` n=(sin((A+D)/(2)))/(sin (A/2))` 
|
|