When a ray of light is incident on the face AB of prism normally, after refraction it is found to graze the side AC as shown in the figure, the refractive index of the prism is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1.414
The ray enters face AB along the normal, so it goes on undeviated. Inside the prism it meets face AC, and the angle between the ray and the normal to AC equals the angle between the normals to the two faces, which is the prism angle at A.
\( \displaystyle \text{Angle of incidence at AC} = \angle A = 45^\circ \)
The ray grazes AC after refraction (angle of refraction \( 90^\circ \)), so this angle of incidence is the critical angle.
\( \displaystyle \sin i_c = \frac{1}{\mu} \;\Rightarrow\; \mu = \frac{1}{\sin 45^\circ} = \sqrt{2} \approx 1.414 \)