Import Question JSON

Current Question (ID: 17493)

Question:

$\text{A plane mirror is placed at the bottom of a fish tank filled with water of refractive index } \frac{4}{3}. \text{ The fish is at a height 10 cm above the plane mirror. An observer } O \text{ is vertically above the fish outside the water. The apparent distance between the fish and its image is:}$

Options:

1. $15 \text{ cm}$
2. $30 \text{ cm}$
3. $35 \text{ cm}$
4. $45 \text{ cm}$

Solution:

$\text{Hint: The apparent height of the fish is given by } h' = \frac{h}{\mu}$ $\text{Step 1: Locate the image of the fish due to the mirror.}$ $\text{Step 2: Use the formula for apparent depth}$ $y = \frac{d}{\mu}$ $y = \frac{d+20}{\mu}$ $\text{Step 3: Find the difference in depth.}$ $\Delta y = y_2 - y_1$ $\Delta y = \frac{d+20}{\mu} - \frac{d}{\mu}$ $\Rightarrow \Delta y = 15 \text{ cm}$ $\text{Hence, option (1) is the correct answer.}$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}