Import Question JSON

Current Question (ID: 17564)

Question:

$\text{If a light ray is incident normally on face } AB \text{ of a prism, then for no emergent ray from second face } AC:$ $[\mu \rightarrow \text{ refractive index of glass of prism}]$

Options:

1. $\mu = \frac{2}{\sqrt{3}}$
2. $\mu > \frac{2}{\sqrt{3}}$
3. $\mu < \frac{2}{\sqrt{3}}$
4. $\mu \text{ can have any value.}$

Solution:

$\text{For no emergent ray, the condition is that the angle of refraction at face } AC \text{ should be greater than the critical angle.}$ $\text{The critical angle } C \text{ is given by } \sin C = \frac{1}{\mu}. \text{ For the prism angle } A = 50^\circ, \text{ the condition becomes:}$ $\mu > \frac{1}{\sin 50^\circ} = \frac{2}{\sqrt{3}}.$

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
}