Import Question JSON

Current Question (ID: 17514)

Question:

$\text{A glass slab is placed with the right-angled prism as shown in the figure. The possible value of } \theta \text{ such that light incident normally on the prism does not pass through the glass slab is:}$

Options:

1. $30^\circ$
2. $37^\circ$
3. $45^\circ$
4. $\text{Both (1) \& (2)}$

Solution:

$\text{Hint: } r_2 \geq \text{critical angle}$ $\text{Step 1: Find the critical angle for the prism-glass interface.}$ $\sin C = \frac{\mu_2}{\mu_1}$ $\sin C = \frac{1.2}{1.5} = \frac{4}{5}$ $C = 53^\circ$ $\text{Step 2: Draw the ray diagram showing total internal reflection at the interface.}$ $90^\circ - \theta \geq C$ $90^\circ - \theta \geq 53^\circ$ $\theta \leq 37^\circ$

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
}