OlympIQ
Read before you solve · 3 min

Read Semicircular Optics: Use the Local Radius as Normal

This short read prepares one exact NSEP pattern: refraction through a semicircular sheet. Identify the physical condition before calculating.

NSEP · Ray Optics · 1 linked question · 100% coverage
Know this first

Refraction through a Semicircular Sheet is the central idea in this question pattern. Identify the condition in the stem before applying the method below.

Study deeper: NCERT Physics · Ray Optics

Start with the physical model

Read the configuration once, state the conserved quantity or governing law, and mark any changing geometry, sign convention or limiting condition.

Build the relation

At the flat face, Snell's law with
i = 45° and µ=√2 gives the refracted angle r=30°

The internal rays are parallel. At the curved surface, the local normal is radial, so the incidence there depends on θ.

Requiring the incidence to be below the critical angle
C = sin-1(1/√2)=45° gives the emergence range 75° ≤ θ ≤ 165°, so A

This range changes if µ changes, hence C.

Geometrically, all emergent rays intersect the reference line OP drawn for
θ = 120°, so D is also correct

B is false. Correct A,C,D.

Check before selecting

Check units, sign and one limiting case. A valid result must still fit the original geometry and stated constraint.

OlympIQ exam lens

  • ✓Name the governing law before using a formula.
  • ✓Keep the stated geometry and direction information explicit.
  • ✓Use one unit or limiting-case check.
OlympIQ trap

At the curved face the normal changes point by point, so one incidence angle cannot describe all rays.

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