Import Question JSON

Current Question (ID: 17572)

Question:

$\text{If there is no emergent light through a prism of refracting angle } 60^\circ, \text{ whatever may be the angle of incidence, then the minimum value of the refractive index of the material of the prism is:}$

Options:

1. $2$
2. $\sqrt{2}$
3. $1.5$
4. $\sqrt{3}$

Solution:

$\text{For no emergent ray in any case, } r_1 \text{ can have the maximum value in the limiting case.}$ $\text{For this, } \angle i = 90^\circ \text{ and } r_1 = r_2 = i_c$ $\Rightarrow 2i_c = A$ $\Rightarrow i_c = 30^\circ$ $\text{Using Snell's law at the second face -}$ $\Rightarrow \mu \sin i_c = 1 \sin 90^\circ$ $\Rightarrow \mu = \frac{1}{\sin 30^\circ} = 2$

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
}