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Current Question (ID: 17570)

Question:

$\text{A ray of light is incident on an equilateral prism at an angle of incidence } i \text{ such that it is incident normally on other refracting faces. Find } i. \ [\text{Take } \mu_{\text{glass}} = 2]$

Options:

1. $30^\circ$
2. $45^\circ$
3. $60^\circ$
4. $\text{Not possible}$

Solution:

$\text{Hint - For an equilateral prism, } A = 60^\circ$ $\text{Step 1: Draw ray diagram}$ $\text{Step 2: Apply Snell's law at first face}$ $\sin i = \mu \sin r$ $\sin i = 2 \times \frac{\sqrt{3}}{2}$ $\sin i = \sqrt{3} \ (\text{not possible})$

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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
}