Question

Derive the expression for the angle of deviation for a ray of light passing through an equilateral prism of refracting angle A.

Answer 1

The angle of deviation for alight passing through an equilateral prism of refracting angle A is given by d = A(n-1).

Consider a thin equilateral prism of angle A.

Let,

The refractive index of the glass of prism be n

The angle of incidence is i1.

The angle of refraction on the first face is r1.

The angle of incidence on the second face is r2.

The angle of emergence is e.

The angle of deviation is d.

Now we know that

d = (i1 + e) - A         (1)

also,

r1 + r2 = A               (2)

We have considered a thin prism, so all the angles will be small and we can assume values of sin∅ = ∅.

Now, by Snell's law, we know that

n = $\frac{sin(i1)}{sin(r1)}$

⇒ n = $\frac{i1}{r1}$

⇒ i1 = nr1

Similarly,

n = $\frac{sin(e)}{sin(r2)}$

⇒ n = $\frac{e}{r2}$

⇒ e = nr2

putting these values of i1 and e in equation (1)

d = nr1 + nr2 - A

d = n(r1+r2) - A

d = nA - A    (r1 + r2 = A)

d = A(n-1)