A laser beam is incident at an angle of 350 from the vertica

A laser beam is incident at an angle of 35.0° from the vertical onto a solution of corn syrup in water. The beam is refracted to 26.24° from the vertical. (a) What is the index of refraction of the corn syrup solution? 1.3 (b) Assume that the light is red, with vacuum wavelength 632.8 nm. Find its wavelength in the solution.487.78 nm (c) Find its frequency in the solution? 4.7408e^14 Hz but its wrong (d) Find its speed in the solution? 2.313e^8 m/s not the right answer

Solution

a) From Snell\'s law

sin i / sin r = n₂ / n₁

sin 35 / sin 26.24 = n₂ / 1

n₂ = 1.298 = 1.30

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b) n₂ / n₁ = lambda₁ / lambda₂

lambda₂ = (n₁ / n₂) * lambda₁

= (1/1.30) * 632.8 = 486.77 nm

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c) f = c / lambda₁ = 3 * 10⁸ / (632.8 x 10^-9) = 4.74 * 10¹⁴ Hz

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d) v = (n₁/n₂ ) * c = ( 1/1.30) * 3 * 10⁸ = 2.31 x 10⁸ m/s