Import Question JSON

Current Question (ID: 17559)

Question:

$\text{The refracting angle of a prism is } A, \text{ and refractive index of the material of the prism is } \cot\left(\frac{A}{2}\right). \text{ The angle of minimum deviation is:}$

Options:

1. $180^\circ - 3A$
2. $180^\circ - 2A$
3. $90^\circ - A$
4. $180^\circ + 2A$

Solution:

$\text{As we know that;}$ $\mu = \frac{\sin\left(\frac{A + D_m}{2}\right)}{\sin\left(\frac{A}{2}\right)} \Rightarrow \cot\frac{A}{2} = \frac{\sin\left(\frac{A + D_m}{2}\right)}{\sin\frac{A}{2}}$ $\Rightarrow \cos\frac{A}{2} = \sin\left(\frac{A + D_m}{2}\right) \Rightarrow \cos\frac{A}{2} = \sin\left(\frac{A + D_m}{2}\right)$ $\Rightarrow \sin\left(\frac{\pi}{2} - \frac{A}{2}\right) = \sin\left(\frac{A + D_m}{2}\right) \Rightarrow \frac{\pi}{2} - \frac{A}{2} = \frac{A + D_m}{2}$ $\Rightarrow D_m = \pi - 2A$

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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
}