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Current Question (ID: 17571)

Question:

$\text{A ray of light incident on a prism of angle } A \text{ and refractive index } \mu \text{ will not emerge out of the prism for any angle of incidence, if:}$ $1. \ \mu > \sin \frac{A}{2}$ $2. \ \mu > \cos A$ $3. \ \mu < \frac{1}{\sin A}$ $4. \ \mu > \frac{1}{\sin \frac{A}{2}}$

Options:

1. $\mu > \sin \frac{A}{2}$
2. $\mu > \cos A$
3. $\mu < \frac{1}{\sin A}$
4. $\mu > \frac{1}{\sin \frac{A}{2}}$

Solution:

$\text{For no emergent ray, } e = 90^\circ$ $\text{So, } r_2 > C.$ $\text{Also, } r_{1\text{max}} = C \text{ for } i = 90^\circ$ $\text{So in total internal reflection,}$ $r_1 + r_2 > 2C$ $A > 2C$ $\text{or, } \frac{A}{2} > C$ $\text{And } \mu = \frac{1}{\sin C}$ $\text{If a ray of light will not emerge out of prism then,}$ $\mu > \frac{1}{\sin C}$ $\Rightarrow \mu > \frac{1}{\sin \frac{A}{2}}$

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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
}