Import Question JSON

Current Question (ID: 17538)

Question:

$\text{Two convex lenses of focal length } X \text{ and } Y \text{ are placed parallel to each other.}$ $\text{An object at infinity from the first lens forms its image at infinity from the}$ $\text{second lens. The separation between the two lenses should be:}$

Options:

1. $X + Y$
2. $\frac{X + Y}{2}$
3. $X - Y$
4. $\frac{X - Y}{2}$

Solution:

$\text{Hint: The system effectively behaves as a single lens with a focal point at}$ $\text{infinity.}$ $\text{Explanation: When two convex lenses with focal lengths } X \text{ and } Y \text{ are}$ $\text{placed parallel to each other, the effective focal length } F \text{ of the system is}$ $\text{determined by the separation } d \text{ between the lenses.}$ $\text{Since the object is at infinity for the first lens and forms an image at infinity}$ $\text{from the second lens, it indicates that the system effectively behaves as a}$ $\text{single lens with a focal point at infinity. This setup requires that the}$ $\text{separation } d \text{ between the lenses equal the sum of their focal lengths.}$ $\text{The image formed by the first lens should lie at the focus of the second lens.}$ $\text{The first image is formed at } X \text{ distance from the first lens and the second}$ $\text{lens should lie at } Y \text{ distance from this point. So, the total distance}$ $= X + Y.$ $\text{Hence, option (1) is the correct answer.}$

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
}