Import Question JSON

Current Question (ID: 17568)

Question:

$\text{A ray of light is incident at an angle of incidence, } i, \text{ on one face of a prism of angle } A \text{ (assumed to be small) and emerges normally from the opposite face.}$ $\text{If the refractive index of the prism is } \mu, \text{ the angle of incidence } i \text{ is nearly equal to:}$

Options:

1. $\mu A$
2. $\frac{\mu A}{2}$
3. $\frac{A}{\mu}$
4. $\frac{A}{2\mu}$

Solution:

$\text{Given,}$ $\text{Angle of incidence } = i$ $\text{Angle of prism } = A$ $\text{Angle of emergence } = 0$ $\text{Refractive index of prism } = \mu$ $\text{Refractive index:}$ $\mu = \frac{\sin i}{\sin r}$ $\mu = \frac{i}{r} \sin A$ $\text{In the case of small-angle:}$ $\mu = \frac{i}{r}$ $i = \mu A$

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
}