In a physics lab, light with a wavelength of 550 nm travels in air from a laser

Question

In a physics lab, light with a wavelength of 550 nm travels in air from a laser to a photocell in a time of 17.2 ns. When a slab of glass with a thickness of 0.870 m is placed in the light beam, with the beam incident along the normal to the parallel faces of the slab, it takes the light a time of 21.1 ns to travel from the laser to the photocell. What is the wavelength of the light in the glass? Use 3.00×108 m/s for the speed of light in a vacuum. Express your answer using two significant figures.

Explanation / Answer

Originally, that 0.870 m distance was air and the light took:

time = distance / speed = 0.870/ 3 x 108 = 2.9 ns to go that distance

Now the light takes an additional    21.1 -17.2 = 3.9 ns   to cover that same distance through the glass.

So the time to travel through the glass is   3.9 + 2.9 = 6.8 ns

Notice the light took  6.8 / 2.9 = 2.345 times longer to get through the glass.

So its speed in the glass must have been 2.345 times slower.

So the index of refraction of the glass is 2.345

And now the wavelength in the glass is the original wavelength divided by the index of refraction:

     550 nm / 2.345 = 234.5nm

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