According to Snell's law, the ratio of sin(i) to sin(r) is equal to the ratio of:

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The correct answer is Option A: Refractive indices of the two media. Snell's Law states that the ratio of the sine of the angle of incidence ($i$) to the sine of the angle of refraction ($r$) is equal to the ratio of the refractive indices of the two media. Mathematically, it is expressed as $rac{\sin(i)}{\sin(r)} = n_2 / n_1$.

Step-by-Step Solution & Concepts:
Snell's Law states that the ratio of the sine of the angle of incidence ($i$) to the sine of the angle of refraction ($r$) is equal to the ratio of the refractive indices of the two media. Mathematically, it is expressed as $ rac{\sin(i)}{\sin(r)} = n_2 / n_1$.

Working Principle: When light travels from one medium to another, it changes speed due to the change in optical density, causing the light ray to bend. The refractive index $n$ is defined as the ratio of the speed of light in a vacuum to the speed in the medium ($n = c / v$). Consequently, the relationship holds that $ rac{\sin(i)}{\sin(r)} = rac{v_1}{v_2} = rac{n_2}{n_1}$, establishing the inverse relationship between the angle and the refractive index.

Key Formulas: $ rac{\sin(i)}{\sin(r)} = rac{n_2}{n_1} = {^1n_2}$ — Snell's Law; $n = rac{c}{v}$ — Definition of refractive index

Key Points: Snell's Law is valid for light rays passing between any two isotropic media.; The frequency of light remains constant when it passes from one medium to another.; Refraction occurs because of the change in the velocity of light.

Advantages: Predicts the trajectory of light rays in optical systems.; Essential for designing lenses and prisms.

Disadvantages: Does not account for non-linear optical effects.; Assumes the medium is isotropic and homogeneous.

Applications: Fiber optic communications; Spectroscopy and lens manufacturing

Additional Info: The constant ratio is also known as the refractive index of the second medium with respect to the first (${^1n_2}$).. Option B and C are related to the law, but the direct definition of the ratio $ rac{\sin(i)}{\sin(r)}$ is the ratio of refractive indices (or the refractive index of medium 2 relative to medium 1).. Frequency (Option D) does not change during refraction, so it cannot describe the ratio of sines.

Answer: A is correct — According to Snell's Law, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant equal to the refractive index of the second medium with respect to the first.

Exam Tip: Always remember that during refraction, the speed and wavelength of light change, but the frequency remains constant as it is a property of the light source.

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Option B: Velocities of light in the two media

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Option C: Wavelengths of light in the two media

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Option D: Frequencies of light in the two media

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