When a glass lens with `mu` = 1.47 is immersed in a trough of liquid, it looks to be disappeared. The liquid in the trough could be

Options

A. Water
B. Kerosene
C. Glycerin
D. Alcohol

Answer

To determine the liquid in which the glass lens appears to disappear, we can follow these steps:

### Step 1: Understand the condition for disappearance
When a lens appears to disappear in a medium, it means that the refractive index of the lens is equal to the refractive index of the medium. This makes the lens effectively invisible as light does not refract at the boundary.

### Step 2: Identify the refractive index of the lens
The given refractive index (μ) of the glass lens is 1.47.

### Step 3: Set up the equation for disappearance
For the lens to appear to disappear in the liquid, we set the refractive index of the liquid (μ_liquid) equal to the refractive index of the lens (μ_lens):
\[ \mu_{liquid} = \mu_{lens} = 1.47 \]

### Step 4: Check the options provided
We need to compare the refractive index of the given liquids with 1.47:
- Water: μ = 1.33
- Kerosene: μ = 1.39
- Glycerin: μ = 1.47
- Alcohol: μ = 1.37

### Step 5: Identify the correct liquid
From the options:
- Water (1.33) is less than 1.47.
- Kerosene (1.39) is less than 1.47.
- Glycerin (1.47) is equal to 1.47.
- Alcohol (1.37) is less than 1.47.

Since only glycerin has a refractive index equal to that of the lens, the liquid in the trough must be glycerin.

### Final Answer:
The liquid in the trough could be **glycerin**.

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