Import Question JSON

Current Question (ID: 17508)

Question:

$\text{A rod of glass } (\mu = 1.5) \text{ and of the square cross-section is bent into the shape as shown.}$ $\text{A parallel beam of light falls on the plane's flat surface } A \text{ as shown in the figure.}$ $\text{If } d \text{ is the width of a side and } R \text{ is the radius of a circular arc}$ $\text{then for what maximum value of } \frac{d}{R}, \text{ light entering the glass slab through the surface } A \text{ will emerge from the glass through } B?$

Options:

1. $1.5$
2. $0.5$
3. $1.3$
4. $\text{None of these}$

Solution:

$\text{Hint: } \sin \theta_c = \frac{1}{\mu}$ $\text{Step: Find the maximum value of } \frac{d}{R}. \text{ All of the rays from the surface } A \text{ will reach the surface } B \text{ only if all of the light rays undergo total internal reflection.}$ $\sin \theta_c = \frac{R}{R+d}$ $\sin \theta_c = \frac{1}{\mu}$ $\frac{1}{\mu} = \frac{R}{R+d} \Rightarrow 1 + \frac{d}{R} = \frac{3}{2}$ $\Rightarrow \frac{d}{R} = 0.5$ $\text{Hence, option (2) is the correct answer.}$

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
}