The electric field of an electromagnetic wave travelling through a...

The electric field is $E(x,t) = 25\sin(2.0 \times 10^{15}t - 10^7 x)$ V/m.
This is in the standard form $E = E_0\sin(\omega t - kx)$ where angular frequency $\omega = 2.0 \times 10^{15}$ rad/s and wave number $k = 10^7$ rad/m.
The speed of the wave in the medium is $v = \frac{\omega}{k} = \frac{2.0 \times 10^{15}}{10^7} = 2.0 \times 10^8$ m/s.
The refractive index is defined as $n = \frac{c}{v}$ where $c = 3.0 \times 10^8$ m/s is the speed of light in vacuum.
Therefore, $n = \frac{3.0 \times 10^8}{2.0 \times 10^8} = 1.5$