Import Question JSON

Current Question (ID: 17501)

Question:

$\text{Light enters at an angle of incidence in a transparent rod of refractive index } n. \text{ For what value of the refractive index of the material of the rod, will the light, once entered into it, not leave it through its lateral face whatsoever be the value of the angle of incidence?}$

Options:

1. $n > \sqrt{2}$
2. $1.0$
3. $1.3$
4. $1.4$

Solution:

$\text{Hint: } \sin i = n \sin r$ $\text{Step: Find the value of the angle of incidence.}$ $\text{From the following figure:}$ $r + i = 90^\circ \Rightarrow i = 90^\circ - r$ $\text{For ray not to emerge from the curved surface } i > C$ $(90^\circ - r) > i_c \text{ or } r < (90^\circ - i_c)$ $\text{According to Snell's law}$ $\sin i = n \sin r$ $\sin i < n \sin (90^\circ - i_c)$ $\sin i \cos i_c < n$ $\sin i \sqrt{1 - \sin^2(i_c)} < n$ $\Rightarrow \sin i \sqrt{1 - 1/n^2} < n$ $n^2 - 1 > 1$ $\Rightarrow n > \sqrt{2}$ $\text{Hence, option (1) is the correct answer.}$

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
}