Import Question JSON

Current Question (ID: 17500)

Question:

$\text{The ratio of the velocity of light in a medium to the velocity of light in a vacuum is } \frac{4}{5}. \text{ If the ray of light is emerging from this medium into the air, then the critical angle for this interface of medium and air will be:}$

Options:

1. $30^\circ$
2. $37^\circ$
3. $53^\circ$
4. $45^\circ$

Solution:

$\text{Hint: } \sin i_C = \frac{1}{\mu}$ $\text{Step 1: Find refraction index for the medium}$ $\mu = \frac{c}{v} = \frac{5}{4}$ $\text{Step 2: Find the critical angle}$ $\sin i_C = \frac{1}{\mu} = \frac{4}{5}$ $\sin i_C = \sin^{-1}\left(\frac{4}{5}\right)$ $i_C = 53^\circ$

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
}