Import Question JSON

Current Question (ID: 17506)

Question:

$\text{A fish is a little away below the surface of a lake. If the critical angle is } 49^\circ, \text{ then the fish could see things above the water surface within an angular range of } \theta^\circ \text{ where:}$

Options:

1. $\theta = 49^\circ$
2. $\theta = 90^\circ$
3. $\theta = 98^\circ$
4. $\theta = 24\frac{1}{2}^\circ$

Solution:

$\text{Hint: Use the concept of total internal reflection.}$ $\text{Step: Find the angular range of } \theta^\circ.$ $\text{From the diagram;}$ $\text{The angular range } \theta = 2 \times \text{ critical angle}$ $\Rightarrow \theta = 2 \times 49^\circ = 98^\circ.$ $\text{Thus the angular range is } 98^\circ.$ $\text{Hence, option (3) is the correct answer.}$

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
}