Question

Derive prism formula with labelled diagram​

Answer 1

Answer:

HOPE U UNDERSTAND

Answer 2

Refer to the attachment for the well labelled diagram of prism.

Derivation:

A clear, polished flat optical element that reflects light is referred to as a prism in physics.

By snell's law,

μ= $\frac{sini}{sinr}$

δ= i₁ - r₁ + i₂ - r₂  ..........(1)

δ= i₁ + i₂ -(r₁+r₂)

∠ALO + ∠AMO= 2rt∠s (as in a quadrilateral ∠ALO =∠AMO = 90°)

∠LAM + ∠LOM = 2rt ∠s ( as the sum of four angles of a quadrilateral =4rt∠s)

∠r₁ + ∠r₂ +∠LOM = 2rt ∠s

∠LAM = ∠r₁ + ∠r₂ ( comparing 1 and 2)

A= ∠r₁ + ∠r₂

δ= i₁ + i₂ - A ( subsitituting A in 1)

i₁ + i₂ = A +δ

∠i₁ + ∠i₂

∠r₁= ∠r₂ = ∠r

∠ALM = ∠LMA= 90° - ∠r

So, AL=LM and LM II BC

∠A= ∠r₁ + ∠r₂

A= 2r as, ∠r₁ =∠r₂=∠r

r= A/2

i₁ + i₂ = A +δ

i₁ + i₁ = A +

2i₁ = A+ δm

i₁ = A+δm/2

Therefore, μ = $\frac{sin\frac{A+deltam}{2} }{\frac{sin A}{2} }$

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