Question

Derive prism formula with the
help of a neat ray diagram,
hence obtain an expression
for the refractive index of a
material of a Prism​

Answer 1

Answer:

Derive the expression for refractive index of the material of the prism in terms of angle of the prism and angle of minimum deviation.

Answer 2

Explanation:

Derivation of prism formula

μ=sinisinr (by Snell’s law)

δ=i1−r1+i2−r2… (eq.1)

δ=i1+i2−(r1+r2) ∠ALO+∠AMO=2rt∠s (from quadrilateral and ∠ALO=∠AMO=90°)

∠LAM+∠LOM=2rt∠s (sum of four ∠s of a quadrilateral = 4 rt∠s) (eq.2)

∠r1+∠r2+∠LOM=2rt∠s (eq.3)

∠LAM=∠r1+∠r2 (comparing eq.2 and eq.3)

A=∠r1+∠r2 δ=i1+i2−A (substituting A in eq.1)

i1+i2=A+δ ∠i1=∠i2 ∠r