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Current Question (ID: 17513)

Question:

$\text{A plane mirror is placed horizontally inside water } \left( \mu = \frac{4}{3} \right).$ $\text{A ray falls normally on it. Then the mirror is rotated through an angle } \theta.$ $\text{The minimum value of } \theta \text{ for which the ray does not come out of the water surface is:}$

Options:

1. $\frac{\pi}{4}$
2. $\sin^{-1}\left(\frac{3}{4}\right)$
3. $\frac{1}{2} \sin^{-1}\left(\frac{3}{4}\right)$
4. $2 \sin^{-1}\left(\frac{3}{4}\right)$

Solution:

$\text{Hint: Total internal reflection will take place.}$ $\text{Step 1: Draw the ray diagram for the given condition.}$ $\text{Step 2: Find the critical angle.}$ $\sin C = \frac{1}{\mu} = \frac{3}{4}$ $\text{Step 3: Relate critical angle and } \theta.$ $2\theta = \sin^{-1}\left(\frac{3}{4}\right)$

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
}