A ray of light travelling in medium 1 strikes medium 2 at an angle of 31 degrees. The ray then refracts within medium 2 at an angle of 24.4. If the speed of light in medium 2 is 1.76 x 108 m/s, what is the index of refraction of medium 1?

Question

A ray of light travelling in medium 1 strikes medium 2 at an angle of 31 degrees. The ray then refracts within medium 2 at an angle of 24.4.  If the speed of light in medium 2 is 1.76 x 108 m/s, what is the index of refraction of medium 1?

BlackTom AI · Accepted Answer

We start by restating the given scenario and known quantities in the problem. A ray passes from medium 1 into medium 2. The angle of incidence in medium 1 is 31 degrees, and the refracted angle in medium 2 is 24.4 degrees. The speed of light in medium 2 is 1.76 x 10^8 m/s. We are to find the index of refraction of medium 1.

First, determine the refractive index of medium 2 using the relationship n = c / v, where c is the speed of light in vacuum (~3.00 x 10^8 m/s). So n2 = (3.00 x 10^8) / (1.76 x 10^8) ≈ 1.7045.

Next, apply Snell's law at the interface: n1 sin(theta1) = n2 sin(theta2), where theta1 is the angle of incidence (31°) and theta2 is the angle of refraction (24.4°).

Solve for n1: n1 = n2 sin(theta2) / sin(theta1).

Compute the sines: sin(24.4°) ≈ 0.414 and sin(31°) ≈ 0.515.

Plug in the values: n1 ≈ 1.7045 * (0.414 / 0.515).

Calculate the ratio 0.414 / 0.515 ≈ 0.804, and multiply by 1.7045 to get n1 ≈ 1.37.

Therefore, the index of refraction of medium 1 is approximately 1.37.

Note on units and consistency: the result uses standard electromagnetic relations and consistent use of c for vacuum light speed, and the given speeds, angles, and resultant n1 are all dimensionally coherent. A small rounding difference in sine values would still yield a value near 1.37.

Physics 1 Hon - Bowles - p06/p07 P10.2/10.22 Optics Formula Practice

A ray of light travelling in medium 1 strikes medium 2 at an angle of 31 degrees. The ray then refracts within medium 2 at an angle of 24.4. If the speed of light in medium 2 is 1.76 x 108 m/s, what is the index of refraction of medium 1?

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