Import Question JSON

Current Question (ID: 17569)

Question:

$\text{For the angle of minimum deviation of a prism to be equal to its refracting angle, the prism must be made of a material whose refractive index:}$

Options:

1. $\text{lies between } \sqrt{2} \text{ and } 1.$
2. $\text{lies between } 2 \text{ and } \sqrt{2}$
3. $\text{is less than } 1.$
4. $\text{is greater than } 2.$

Solution:

$\mu = \frac{\sin \left( \frac{A + \delta_m}{2} \right)}{\sin \left( \frac{A}{2} \right)} = \frac{\sin \left( \frac{A + A}{2} \right)}{\sin \left( \frac{A}{2} \right)}$ $\text{In the given situation, the value of } A \text{ varies from } 0 \text{ to } 90^\circ.$ $\text{So, } \mu_{\text{min}} = 2 \cos \frac{90^\circ}{2} = \sqrt{2}$ $\text{and } \mu_{\text{max}} = 2 \cos 0^\circ = 2$

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
}