Question

Define the term, "refractive index" of a medium. Verify Snell’s law of refraction when a plane wave front is propagating from a denser to a rarer medium.

Answer 1

Explanation:

Refractive index measures the bending of a ray of light when it passes from one medium to another. It is defined as the ratio of speed of light in air to the speed of light in the medium or speed of light in medium 1 to medium 2. where c is the speed of light in air, v is speed of light in medium – v1 is the speed in medium 1 and v2 is the speed in medium 2. It is also defined as the ratio of the sine of angle of incidence to sine of angle of refraction. where i is angle of incidence and r is the angle of refraction. Now, we will verify Snell’s law of refraction when plane wavefront is propagating from denser to a rarer medium. Consider following figure: • XY is the interface between denser medium and rarer medium. • AB is plane wavefront incident on XY at angle of incidence i. • Let v1 be velocity of light in denser medium and v2 be velocity of light in rarer medium (v1 < v2). • According to Huygens principle, every point on AB is source of secondary wavelets. Suppose wavelets from B reach B′ on XY in t seconds. Wavelets from A reach point A in rarer medium in t seconds and in the same time, the wavelets at point D reach point D′ in rare medium. Therefore A'B' represents the refracted wavefront at XY plane at angle of refraction r. Time taken by light to travel a point on incident wavefront to a corresponding point in refracted wavefront should be equal. Time taken by light to go from D to D' is Now, the time taken by secondary wavelets to travel distance DP in denser medium and PD′ in rarer medium is equal to the time taken by secondary wavelets to travel distance A′ in rarer medium. Therefore, Equating Eqs. (1) and (3), we get From the right-angled triangle ADP, we have ∠ DAP = i ⇒ DP = AP sin i Similarly, from the in right-angled triangle AN′P, we get ∠ N'PA = r ⇒ AN' = AP sin r Substituting value of DP and AN′ in Eq. (4), we get Therefore, This is Snell’s law of refraction

Answer 2

Refractive index is a property of a medium that describes how much the speed of light is reduced when it passes through that medium compared to its speed in a vacuum. It is defined as the ratio of the speed of light in a vacuum to the speed of light in the medium. The refractive index of a medium is denoted by the symbol n.

• Mathematically, n = c/v, where c is the speed of light in vacuum and v is the speed of light in the medium.
• When a plane wave front is propagating from a denser to a rarer medium, Snell's law of refraction describes the relationship between the incident angle, the refracted angle, and the refractive indices of the two media.

The law states that: n1 sinθ1 = n2 sinθ2

• where n1 and n2 are the refractive indices of the two media, θ1 is the angle of incidence of the wavefront, and θ2 is the angle of refraction.
• To verify Snell's law of refraction, consider a plane wave front of light propagating from a denser medium (such as water) to a rarer medium (such as air).

Here's how the law can be verified:

• Measure the angle of incidence of the wavefront, θ1, with respect to the normal to the interface between the two media.
• Measure the angle of refraction, θ2, with respect to the normal to the interface.
• Calculate the refractive indices of the two media using n1 = c/v1 and n2 = c/v2, where c is the speed of light in vacuum and v1 and v2 are the speeds of light in the two media, respectively.
• Verify that n1 sinθ1 = n2 sinθ2, which means that the law of refraction is satisfied.

• In summary, the refractive index of a medium describes how much the speed of light is reduced when it passes through that medium. Snell's law of refraction describes the relationship between the incident angle, the refracted angle, and the refractive indices of the two media when a plane wave front propagates from a denser to a rarer medium. This law can be verified experimentally by measuring the angles of incidence and refraction and calculating the refractive indices of the media.

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