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Question #43143

Difficulty: 8/10 | 🟢 Free

The Question

A thin prism of refractive index $n = 1.5$ is placed at the origin of a Cartesian coordinate system. The first face of the prism lies in the $yz$ -plane ( $x=0$ ). The outward normal to the second face of the prism is given by the unit vector $\hat{n}_2 \approx \hat{i} + \alpha \hat{j} + \beta \hat{k}$ , where $\alpha = 0.03$ rad and $\beta = 0.04$ rad. A paraxial beam of light, traveling generally in the $+x$ direction, is incident on the first face. The beam is converging towards a virtual point object $P$ located at $(100 \text{ cm}, 2 \text{ cm}, -1 \text{ cm})$ . After passing through the prism, the beam converges to a new real point $P'$ . Find the coordinates of $P'$ .

Options

A.
$(100 \text{ cm}, 0.5 \text{ cm}, -3.0 \text{ cm})$
B.
$(100 \text{ cm}, 3.5 \text{ cm}, 1.0 \text{ cm})$
C.
$(-100 \text{ cm}, 3.5 \text{ cm}, 1.0 \text{ cm})$
D.
$(100 \text{ cm}, -0.5 \text{ cm}, -1.0 \text{ cm})$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Dispersion vs Deviation|Virtual Object Trap|Vector Cross-Product

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to apply Snell's Law in its vector form under the small-angle approximation, specifically targeting the 'Virtual Object Trap'.

Students commonly memorize the scalar deviation formula $\delta = (n-1)A$ and struggle to apply it in 3D space.

Furthermore, by presenting a virtual object (rays converging to a point behind the prism), students who rely on standard ray-tracing diagrams often misassign the sign of the incident angle or treat the convergence point as a real source, leading to inverted deviation vectors.

The correct approach requires recognizing that the deviation vector $\vec{\delta} = -(n-1)\vec{A}$ must be added to the incident ray's direction vector $\vec{\theta}_1$ , preserving the positive $x$ -propagation of the converging beam.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Ray Optics and Optical Instruments - Class 12
Concept	Dispersion vs Deviation
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free