Import Question JSON

Current Question (ID: 17561)

Question:

$\text{The angle of minimum deviation for a glass prism of refractive index } \mu = \sqrt{3} \text{ equals the refracting angle of the prism. The angle of the prism is:}$

Options:

1. $30^\circ$
2. $60^\circ$
3. $90^\circ$
4. $45^\circ$

Solution:

$\text{Hint: } \delta_m = i + e - A$ $\text{Step: Find the angle of the prism.}$ $\text{For minimum deviation, } \angle r_1 = \angle r_2 = \frac{A}{2}$ $\Rightarrow \text{Minimum deviation, } \delta_m = i + e - A$ $\Rightarrow 2A = 2i \Rightarrow A = i$ $\text{Using Snell's law:}$ $\sin i = \mu \sin r_1 \Rightarrow \sin A = \sqrt{3} \sin \frac{A}{2}$ $\Rightarrow 2 \sin \frac{A}{2} \cdot \cos \frac{A}{2} = \sqrt{3} \sin \frac{A}{2}$ $\Rightarrow \cos \frac{A}{2} = \frac{\sqrt{3}}{2} = \cos 30^\circ \Rightarrow A = 60^\circ$ $\text{Therefore, the angle of the prism is } 60^\circ.$ $\text{Hence, option (2) is the correct answer.}$

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
}