PrayogX › Physics › Ray Optics and Optical Instruments

Two isosceles prisms linked by a mirror - minimum deviation conditions and the angle between the apex bisectors

A ray passes through two isosceles prisms whose facing sides are perpendicular to a mirror, so i2 = e1. Testing each statement by exact ray tracing: (A) true, (B) false, (C) true (theta is between the apex bisectors, (A1 + A2)/2), (D) true - answer (A), (C), (D).

Sub-topics covered

• Refraction through a prism: deviation i + e - A
• Minimum deviation: the symmetric path, sin i = n sin(A/2)
• Plane-mirror reflection between faces perpendicular to the mirror: i2 = e1
• Thin prisms: deviation (n - 1)A
• Reading a ray diagram: the bisector of an isosceles prism's apex angle

What it teaches

• Faces a1b1 and a2b2 are both perpendicular to the mirror, so the reflection carries the emergence angle of prism 1 into the incidence angle of prism 2: i2 = e1
• (D) true: prism 1 at minimum deviation gives sin e1 = n1 sin(A1/2), hence sin i2 = n1 sin(A1/2) whatever prism 2 is
• (A) true: both at minimum deviation requires n1 sin(A1/2) = n2 sin(A2/2), i.e. n2/n1 = sin(A1/2)/sin(A2/2)
• (B) false: sin i1 = n2 sin(A2/2) would need prism 1 symmetric as well - a counter-example is found
• (C) true: the dashed lines are the apex-angle bisectors (they meet the bases at right angles), so theta = (A1 + A2)/2 = dm1/(2(n1 - 1)) + dm2/(2(n2 - 1)) for thin prisms
• Trap: reading theta between the extended faces gives A1 + A2 and wrongly rejects (C)

Simulation ID

• ADV-2026-P2-PHY-Q05 · revision 1

See this simulation in the library →  ·  open the simulation file on its own