Question

calculate the speed of of light in quartz

Answer 1

$\eta$ = Speed of light in air/ Speed of light in medium

/eta = 3 * 10^8/ v

/eta for quartz = 1.458 = 3 * 10^8 /v

therefore v = 3 * 10^8 /1.458 = 2.057 * 10^8 m/s

speed of light in quartz is less than speed of light in air

Answer 2

The speed of light is fixed for a given medium. So, for your fused quartz, c = Cn, where C is the speed in a vacuum and n is the refraction index, which you need to look up. c = ? is the answer you are looking for.

Note this has nothing... nothing... to do with L, the wavelength of the light. L = CT, where C is light speed and T is the period of the light wave. As f = 1/T is the frequency of any wave, we have Lf = C. So as you can see, whenever the wavelength is changed, the frequency must also change to keep the light speed at C, no matter what.

We can write L = CT = (c/n)T; so that c = nL/T, but you still need n the refraction index and this is just a variation of c = nC anyway

Answer 3

speed of light in a medium of refractive index n is given by V =nC , C-speed of light = 3 x 10⁸ m/s
refractive index of quartz = 1.46 therefore V= 1.46 x 3 x 10⁸ = 4.38 x 10⁸ m/s