 A monochromatic light ray passes through a prism of refracting angle $A = 60°$ at minimum deviation. If the angle of minimum deviation is $\delta_m = 30°$, find the refractive index of the prism material.
A$1.00$
B$1.33$
C$\sqrt{2}$
D$\sqrt{3}$
Answer & Solution
Correct answer: C. $\sqrt{2}$
**Prism formula at minimum deviation:**
$$\mu = \dfrac{\sin\!\left(\dfrac{A + \delta_m}{2}\right)}{\sin\!\left(\dfrac{A}{2}\right)}$$
**Substitute.** $\dfrac{A + \delta_m}{2} = \dfrac{60 + 30}{2} = 45°$ and $\dfrac{A}{2} = 30°$.
$$\mu = \dfrac{\sin 45°}{\sin 30°} = \dfrac{\sqrt{2}/2}{1/2} = \sqrt{2} \approx 1.414$$
Option B (1.33) is water's refractive index — a tempting wrong pick if you guess instead of computing.
Related questions
Two thin convex lenses, each of focal length 20 cm, are placed coaxially 10 cm apart in aiA Galilean telescope (objective convex, eyepiece concave) has objective focal length 20 cmA thin prism of refracting angle 5° is made of glass with n = 1.5. The deviation δ of a liRefraction at a single convex spherical surface: an object in air (n₁ = 1) at distance 20 A converging lens of focal length f is split along its principal axis into two semicirculaA compound microscope has an objective of focal length 1.0 cm and an eyepiece of focal lenGlass has refractive index 1.5 with respect to air. A light ray inside the glass strikes tThe apparent depth of an object lying at the bottom of a pool of water (n = 4/3) is, in te