Prism DeviationJEE Main

Minimum deviation & dispersion — interactive Physics simulation for IIT-JEE.

Concept

A prism bends light twice and the total deviation depends on the angle of incidence. It reaches a minimum when the ray passes symmetrically — and that minimum deviation lets you measure the glass's refractive index precisely.

Key formula

n = \frac{\sin\!\left(\frac{A+\delta_m}{2}\right)}{\sin\!\left(\frac{A}{2}\right)}, \qquad \text{thin prism: } \delta = (n-1)A

Derivation

At minimum deviation the ray inside the prism is parallel to the base, so the two refractions are symmetric ( $i_1 = i_2$ , $r_1 = r_2 = A/2$ ).

Substituting into Snell's law at one face gives the prism formula. For a small apex angle the deviation simplifies to $\delta = (n-1)A$ , independent of incidence.

Scenarios to explore

Prism Deviation — Minimum deviation and dispersion of white light.

Real-world applications

Spectrometers measuring refractive index.
Splitting white light into a spectrum (dispersion).
Binocular and camera prism systems.

JEE exam tips

At minimum deviation $r_1 = r_2 = A/2$ and $i_1 = i_2$ .
Dispersive power $\omega = (\mu_v - \mu_r)/(\mu_y - 1)$ .
Maximum deviation occurs at grazing incidence.

Common mistakes

Assuming deviation always decreases with incidence (it has a minimum).
Using the thin-prism formula for large apex angles.
Forgetting that different colours have different n (dispersion).

Exam traps to avoid

If $n\sin(A/2) > 1$ the ray undergoes TIR inside — no emergent ray.
Deviation vs incidence is a U-shaped curve, not monotonic.