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General SciencePhysics

A ray of light travels from air into a glass slab with a refractive index of 1.5 · If the angle of incidence is 45 degrees, what is the sine of the angle of refraction?

0.47

0.52

0.61

0.75

Correct Answer

🔬 SC • Science Concept & PrincipleGeneral SciencePhysics

Option A

0.47

Quick Summary:

To determine the sine of the angle of refraction, we apply Snell's Law, which relates the refractive indices and the sines of the angles of incidence and refraction · Given $n_1 = 1.0$ (air), $n_2 = 1.5$ (glass), and $i = 45°$ , we calculate $\sin(r) = \frac{\sin(45°)}{1.5}$ .

🔬SCScience SolutionConcept & Principle

💡 Explanation

💡 Everyday Analogy (Real-World Intuition)

Think of a car moving from a smooth pavement onto a muddy field at an angle; the wheel that hits the mud first slows down, causing the car to pivot or turn towards the normal line of the boundary.

🔢 Key Formulas

$n_1 \sin(i) = n_2 \sin(r)$ — Snell's Law

$\sin(45°) \approx 0.707$ — Trigonometric constant

⚙️ Working Principle

Snell's Law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant, equal to the ratio of the refractive indices of the two media · When light enters an optically denser medium like glass from a rarer medium like air, it bends towards the normal, resulting in a smaller angle of refraction.

📌 Key Points

▸
Light bends towards the normal when traveling from a rarer to a denser medium.
▸
The refractive index is a unitless ratio comparing the speed of light in vacuum to the speed of light in the material.
▸
Since the refractive index of glass is greater than air, the angle of refraction must be less than the angle of incidence.

🛠️ Applications / Uses

▸
Design of lenses for cameras and eyeglasses
▸
Fiber optic communication systems

📄 Additional Information

▸
Calculation: $\sin(r) = \frac{0.707}{1.5} \approx 0.471$ .
▸
Option B (0.52), C (0.61), and D (0.75) are mathematically incorrect based on the application of Snell's Law.

📊 Diagram / Illustration

✅

A is correct — The sine of the angle of refraction is calculated as $0.47$ using the formula derived from Snell's Law.

Core Concepts Used

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Refraction Snell's Law Refractive Index

💡 EXAM TIP

Always remember the value $\sin(45°) = \frac{1}{\sqrt{2}} \approx 0.707$ ; it is a frequently used constant in physics problems involving angles.

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