Question

Derive n = sin (A+D)/2 / sin (A/2) for refraction through a prism.

Answer 1

if you like brainliest please

Answer 2

n = (sin (A+D)÷2) ÷ sin ( A÷2) or  μ = (sin (A+D)÷2) ÷ sin ( A÷2) is the equation for refractive index of a prism

Explanation:

Refractive index is defined as the measurement of bending of ray light when it travels from one to another medium.

It is also called as the index of reflection.

The given figure consists of

OP - Incident ray which is written as $i_1$

QR - emergent angle which is written as $i_2$

A - Angle of prism

In case of minimum deviation, ∠$r_1$ = ∠$r_2$ = ∠rc ----------> (1)

From the figure ,    A = ∠$r_1$ + ∠$r_2$ -----------> (2)

Substitute 2 in 1

Then,   A = ∠r +∠r

            A = 2∠r

Also it can be written as ∠r = A÷2

Again, A + δ = $i_1$ + $i_2$ -----------> (3)

$i_1$ = $i_2$ = i and δ = D  -----------> (4)

Substitute 4 in 3

Then equation 3 can be written as A + D = i + i

                                                          A + D = 2 i

                                                         i = (A + D) ÷ 2 ----------> (5)

Substitute the equation (5) in Snell's law equation

Where Snell's law is defined as the ratio between sin of angle of incidence and sin of angle of refraction and it is denoted as μ or n.

μ = (sin i) ÷ (sin r)

μ = (sin (A +D) ÷2) ÷ ( sin ( A ÷ 2 ))

Also n =  (sin (A +D) ÷2) ÷ ( sin ( A ÷ 2 ))

To learn more ...

1. https://brainly.in/question/2044822