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Current Question (ID: 17518)

Question:

$\text{In a glass } (\mu = 1.5) \text{ sphere with a radius of } 10 \text{ cm, there is an air bubble } B \text{ at a distance of } 5 \text{ cm from } C. \text{ The distance of the bubble from the surface of the sphere (i.e., point } A) \text{ as observed from the point } P \text{ in the air will be:}$

Options:

1. $4.5 \text{ cm}$
2. $20.0 \text{ cm}$
3. $9.37 \text{ cm}$
4. $6.67 \text{ cm}$

Solution:

$\text{Hint: } \frac{n_2}{v} - \frac{n_1}{u} = \frac{n_2-n_1}{R}$ $\text{Step: Find the distance of the bubble from the surface of the sphere}$ $\text{Write } \mu, v, \text{ and } R \text{ according to the sign convention}$ $\mu = -15 \text{ cm}, R = -10 \text{ cm}, n_2 = 1, \text{ and } n_1 = 1.5$ $\text{Use the formula for refraction at the curved interface}$ $\frac{n_2}{v} - \frac{n_1}{\mu} = \frac{n_2-n_1}{R}$ $\frac{1}{v} - \frac{1.5}{-15} = \frac{1-1.5}{-10}$ $\Rightarrow v = -20 \text{ cm}$ $\text{Hence, option (2) is the correct answer.}$

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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
}