Question

A tank is filled with benzene to a height of \(120~\text{mm}\). The apparent depth of a needle lying at the bottom of the tank, as seen through a microscope, is found to be \(80~\text{mm}\). The refractive index of benzene is

• A. 1.5
• B. 2.5
• C. 3.5
• D. 4.5

Hint:

Refractive index \( \mu = \frac{\text{Real Depth}}{\text{Apparent Depth}} \) — use this for problems involving refraction through liquids.

Answer 1

The Correct Option is A

The refractive index \(\mu\) of a medium is given by the ratio of real depth to apparent depth: \[ \mu = \frac{\text{Real Depth}}{\text{Apparent Depth}} \] Here,
- Real depth = \(120~\text{mm}\)
- Apparent depth = \(80~\text{mm}\)
\[ \mu = \frac{120}{80} = 1.5 \] Thus, the refractive index of benzene is 1.5.

Answer 2

Step 1: Understand the problem
- Actual depth of benzene column, \(d = 120~\text{mm}\)
- Apparent depth observed, \(d' = 80~\text{mm}\)
- Refractive index \(n\) of benzene is to be found.

Step 2: Recall the relation between real depth, apparent depth, and refractive index
\[ n = \frac{\text{Real depth}}{\text{Apparent depth}} = \frac{d}{d'} \]

Step 3: Calculate refractive index
\[ n = \frac{120}{80} = 1.5 \]

Step 4: Final answer
The refractive index of benzene is 1.5.