Import Question JSON

Current Question (ID: 17590)

Question:

$\text{In an astronomical telescope in normal adjustment a straight black line of length } L \text{ is drawn on inside part of the objective lens. The eye-piece forms a real image of this line. The length of this image is } l. \text{ The magnification of the telescope is:}$

Options:

1. $\frac{L}{l} + 1$
2. $\frac{L}{l} - 1$
3. $\frac{L+1}{l-1}$
4. $\frac{L}{l}$

Solution:

$\text{We know,}$ $\text{Magnification of the telescope;} \ m = \frac{f_o}{f_e}$ $\text{Here,} \ \frac{f_e}{f_e - u} = -\frac{l}{L}$ $\text{As,} \ u = f_o + f_e$ $\frac{f_e}{f_e - (f_o + f_e)} = -\frac{l}{L} \Rightarrow \frac{f_e}{f_o} = \frac{l}{L}$ $m = \frac{f_o}{f_e} = \frac{L}{l}$

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
}