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NEET 2021 Physics Question 9 Solution

Topic: Ray Optics and Optical Instruments · Official NTA Booklet Code M1

$NEET 2021 Physics Question 9: Refraction Through a Right-Angled Prism: Normal Incidence and Angle of Emergence$

Question

Find the value of the angle of emergence from the prism. Refractive index of the glass is 3.

✓

Verified Against NTA Final Answer Key

Option (1) : 60°

📚 Ray Optics and Optical Instruments Easy

📋 Given Parameters & Problem Setup

Prism Geometry Right-angled prism (Angles: 90°, 60°, 30°)

Incidence Condition Incident normally on hypotenuse face

Refractive Index (μ) √3

⚡

The 30-Second Exam Hall Shortcut: ⚡ Normal Incidence + Snell's Law at Second Face

⏱️ Save ~25 seconds

Normal incidence on hypotenuse $\implies$ ray enters undeviated ( $r_1 = 0$ ). By geometry, ray hits the vertical face at angle of incidence $r_2 = 30^\circ$ . Apply Snell's law: $\mu \sin 30^\circ = 1 \cdot \sin e \implies \sqrt{3} \times \frac{1}{2} = \sin e \implies \sin e = \frac{\sqrt{3}}{2} \implies e = 60^\circ$ ! Match Option (1)!

1 Ray is normal to hypotenuse

\implies

angle of incidence at first face

i_1 = 0^\circ

, angle of refraction

r_1 = 0^\circ

2 Top angle of prism

= 180^\circ - (90^\circ + 60^\circ) = 30^\circ

3 Ray forms right triangle inside: angle between ray and vertical surface

= 60^\circ

4 Normal to vertical surface is horizontal

\implies

angle of incidence at vertical face

r_2 = 90^\circ - 60^\circ = 30^\circ

5 Snell's law at vertical face:

\sqrt{3} \sin 30^\circ = 1 \cdot \sin e \implies \sin e = \frac{\sqrt{3}}{2} \implies e = 60^\circ

6 Match Option (1).

🛡️

Why You Can 100% Trust This Shortcut: Canonical Snell's law of refraction and geometric ray tracing.

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Ray Propagation at the Hypotenuse Face

The incident ray is perpendicular to the hypotenuse face (marked with a right-angle symbol in the diagram). By Snell's law, $\sin i_1 = 0 \implies \sin r_1 = 0$ , so the ray enters the prism without any deviation.

Step 2

Determining the Angle of Incidence at the Second (Vertical) Face

Consider the triangle at the top of the prism: - The apex angle between the vertical face and the hypotenuse is $A = 180^\circ - (90^\circ + 60^\circ) = 30^\circ$ . - The ray enters perpendicular to the hypotenuse, making an angle of $90^\circ$ with the hypotenuse. - Inside the top small triangle, the angle between the ray and the vertical face is $180^\circ - (90^\circ + 30^\circ) = 60^\circ$ . - Since the normal to the vertical face is perpendicular to it, the angle of incidence $r_2$ (angle with the normal) is:

r_2 = 90^\circ - 60^\circ = 30^\circ

Step 3

Applying Snell's Law at the Second Face to Find Angle of Emergence

At the vertical glass-air interface, light travels from glass ( $\mu = \sqrt{3}$ ) into air ( $n = 1$ ):

\mu \sin r_2 = 1 \cdot \sin e \implies \sqrt{3} \sin(30^\circ) = \sin e \implies \sqrt{3} \left(\frac{1}{2}\right) = \sin e \implies \sin e = \frac{\sqrt{3}}{2} \implies e = 60^\circ

⭐

360° Option Elimination Engine Key Feature

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1 1

✓ 100% Correct

Verdict & Scientific Reason:

Exact angle of emergence calculated via Snell's law: $e = \arcsin(\sqrt{3}/2) = 60^\circ$ .

💡

Why this is airtight: None; rigorous geometric optics solution.

2 2

✗ Incorrect

Verdict & Scientific Reason:

This is the internal angle of incidence ( $r_2 = 30^\circ$ ), not the emergent angle into air.

⚠️

Student Fallacy (Why candidates pick this trap): Confusing the internal angle of incidence with the emergent angle.

3 3

✗ Incorrect

Verdict & Scientific Reason:

Result of using $\mu = \sqrt{2}$ instead of $\sqrt{3}$ .

⚠️

Student Fallacy (Why candidates pick this trap): Assuming

\sin e = 1/\sqrt{2}

4 4

✗ Incorrect

Verdict & Scientific Reason:

This would be grazing emergence if $r_2$ equaled the critical angle $\theta_c = \arcsin(1/\sqrt{3}) \approx 35.3^\circ$ . Since $30^\circ < 35.3^\circ$ , refraction occurs normally at $60^\circ$ .

⚠️

Student Fallacy (Why candidates pick this trap): Mistaking the ray path for total internal reflection.

⚠️

NTA Trap Alert: Angle with Surface vs. Angle with Normal Trap

Students frequently take the $60^\circ$ angle between the ray and the glass surface as the angle of incidence, computing $\sqrt{3} \sin 60^\circ = 1.5 > 1$ and falsely concluding Total Internal Reflection occurred.

🛡️ How to avoid the -1 mark: Always draw the NORMAL perpendicular to the surface! The angle of incidence is measured from the normal:

r_2 = 90^\circ - 60^\circ = 30^\circ

📖

Core NEET Syllabus Standard

NCERT Physics · Ray Optics and Optical Instruments Standard Benchmark

Core Scientific Principle Tested:

"Snell's law governs refraction at each boundary: $n_1 \sin \theta_1 = n_2 \sin \theta_2$ . Angles are always measured with respect to the surface normal."

Syllabus Focus: Refraction Through a Prism

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2021 Physics Question 9 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Normal Incidence + Snell's Law at Second Face

Step-by-Step Rigorous Workflow & Mathematical Proof

Ray Propagation at the Hypotenuse Face

Determining the Angle of Incidence at the Second (Vertical) Face

Applying Snell's Law at the Second Face to Find Angle of Emergence

360° Option Elimination Engine Key Feature

NTA Trap Alert: Angle with Surface vs. Angle with Normal Trap

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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