A horizontal ray of light is incident on a right-angled prism with a prism angle of $6^{\circ}$. If the refrac

Question

A horizontal ray of light is incident on a right-angled prism with a prism angle of $6^{\circ}$. If the refractive index of the material of the prism is 1.5, then the angle of emergence will be:

Accepted Answer

1. **Ray Entry:** A horizontal ray of light incident on the vertical face of a right-angled prism falls normally on it (angle of incidence $i = 0^{\circ}$). It passes through undeviated, meaning the angle of refraction at the first face is $r_1 = 0^{\circ}$.
2. **Angle of Incidence at Second Face:** For a prism, the angle of the prism $A$ is related to the internal angles of refraction by $A = r_1 + r_2$. Given $A = 6^{\circ}$, the angle of incidence at the second face is $r_2 = A - r_1 = 6^{\circ} - 0^{\circ} = 6^{\circ}$.
3. **Snell's Law for Emergence:** Applying Snell's law at the second face (from the prism to air): $\mu \sin(r_2) = 1 \cdot \sin(e)$. Since the angles are small, we can use the small-angle approximation $\sin(	heta) \approx 	heta$.
4. **Calculation:** Substituting the given values, $e \approx \mu 	imes r_2 = 1.5 	imes 6^{\circ} = 9^{\circ}$. Therefore, the angle of emergence is $9^{\circ}$.

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