A ray of light passes through a triangular glass prism of angle A kep…

The correct answer is Option (1) → Four

Some prism relations come only from the shape of the prism and Snell’s law. They hold for every ray. Others hold only at minimum deviation, or only for a thin prism.

The relations that hold for every ray:

• \( r_1+r_2=A \) — geometry of the prism

• \( \delta=i+e-A \) — follows from the two deviations

• \( \sin i=n\sin r_1 \) — Snell’s law at the first face

• \( \delta=(i-r_1)+(e-r_2) \) — sum of the deviations at the two faces

The relations that do not:

• \( i=e \) — only at minimum deviation

• \( r_1=r_2 \) — only at minimum deviation

• \( \delta=(n-1)A \) — only for a thin prism at minimum deviation

• \( n=\frac{\sin[(A+\delta)/2]}{\sin(A/2)} \) — only when \( \delta=D_m \)

Number of relations that hold for every ray = 4

NCERT (2026-27):
Refraction Through a Prism – “Comparing these two equations, we get”

    \( \displaystyle r_1+r_2=A \)\( \qquad (9.34) \)

“The total deviation δ is the sum of deviations at the two faces, δ= (i – r₁ ) + (e – r₂ )”

“that is,”

    \( \displaystyle \delta=i+e-A \)\( \qquad (9.35) \)

Refraction – “(ii) The ratio of the sine of the angle of incidence to the sine of angle of refraction is constant. … We have”

    \( \displaystyle \frac{\sin i}{\sin r}=n_{21} \)\( \qquad (9.10) \)

“where n₂₁ is a constant, called the refractive index of the second medium with respect to the first medium.”

Refraction Through a Prism – “At the minimum deviation D_m, the refracted ray inside the prism becomes parallel to its base. We have δ = D_m, i = e which implies r₁ = r₂.”

Refraction Through a Prism – “The refractive index of the prism is”

    \( \displaystyle n_{21}=\frac{n_2}{n_1}=\frac{\sin[(A+D_m)/2]}{\sin[A/2]} \)\( \qquad (9.38) \)

Refraction Through a Prism – “For a small angle prism, i.e., a thin prism, D_m is also very small, and we get …”

    \( \displaystyle D_m=(n_{21}-1)A \)