Silvered Prism – Ray Retracing Its Path
A glass prism (μ = 1.5) has angle A = 35°. Face AC is silvered. A ray is incident on face AB such that after reflection it retraces its path. Find the angle of incidence.
Step 1: Condition for Retracing
If a ray retraces its path after reflection from a silvered face, it must strike that face normally.
Step 2: Prism Geometry
For a prism:
Since r₂ = 0° (normal incidence at AC),
Step 3: Apply Snell’s Law at Face AB
Final Answer
Correct Option: (A) 59.4°
Theory: Ray Retracing in a Silvered Prism
When one face of a prism is silvered, it behaves like a mirror. For a ray to retrace its path completely, it must strike the silvered surface normally (angle of incidence = 0°).
Important Prism Relations
Thus, r₁ becomes equal to the prism angle A.
Frequently Asked Questions
Why must the ray strike the silvered face normally?
Only when the angle of incidence is zero will the reflected ray return exactly along the same path.
Why is r₁ equal to the prism angle?
From prism geometry, r₁ + r₂ = A. Since r₂ = 0° for normal reflection, r₁ = A.
Which law is used to calculate the angle of incidence?
Snell’s law is applied at the first refracting surface AB.
Does the refractive index affect the answer?
Yes. The angle of incidence depends directly on refractive index through Snell’s law.