Define refractive index. You are given kerosene, turpentine, and water. In which of these does light travel faster? Which of these liquids are optically denser? Find out the speed of light in turpentine if the light travels from air to turpentine. The refractive indices of water, kerosene, and turpentine are 1.33, 1.44, and 1.47, respectively. The speed of light in air is 3 × 10⁸ m/s.

1. Definition of Refractive Index:
The refractive index (nn) of a medium is the ratio of the speed of light in a vacuum (cc) to the speed of light in the medium (vv):
n=cvn = \frac{c}{v}
2. Liquid in Which Light Travels Faster:
The speed of light in a medium is inversely proportional to its refractive index. A lower refractive index indicates faster light travel.
Comparing the refractive indices:
• Water: nw=1.33n_w = 1.33
• Kerosene: nk=1.44n_k = 1.44
• Turpentine: nt=1.47n_t = 1.47
Light travels fastest in water because it has the lowest refractive index (nw=1.33n_w = 1.33).
3. Optically Denser Liquids:
The optical density of a medium increases with its refractive index.
Comparing the refractive indices:
• Turpentine (nt=1.47n_t = 1.47) is the most optically dense.
• Water (nw=1.33n_w = 1.33) is the least optically dense.
4. Speed of Light in Turpentine:
From the refractive index formula:
nt=cvtn_t = \frac{c}{v_t}
Rearranging for vtv_t:
vt=cntv_t = \frac{c}{n_t}
Substitute the values:
vt=3×1081.47v_t = \frac{3 \times 10^8}{1.47} vt≈2.04×108 m/sv_t \approx 2.04 \times 10^8 \, \text{m/s}
1. Light travels fastest in water because it has the lowest refractive index (n=1.33n = 1.33).
2. Turpentine is the most optically dense liquid (n=1.47n = 1.47).
3. The speed of light in turpentine is approximately: 2.04×108 m/s.2.04 \times 10^8 \, \text{m/s}.