This problem is based on the principle of a beam expander, which works exactly like an astronomical telescope. When two convex lenses are arranged such that their focal points coincide, a parallel beam entering the first lens emerges as a parallel beam from the second lens.
For a telescope or beam expander, the magnification in terms of diameter is:
\[ M = \frac{D_2}{D_1} \]
Also, angular magnification for two convex lenses is:
\[ M = \frac{f_2}{f_1} \]
Given:
\[ D_1 = 2 \text{ mm} \]
\[ D_2 = 14 \text{ mm} \]
\[ f_1 = 40 \text{ mm} \]
Thus, magnification:
\[ M = \frac{14}{2} = 7 \]
Since:
\[ M = \frac{f_2}{f_1} \]
\[ 7 = \frac{f_2}{40} \]
\[ f_2 = 280 \text{ mm} \]
Correct Answer: 280 mm
A collimated beam means a beam of light whose rays are parallel to each other. When parallel rays fall on a convex lens, they converge at the focal point. If another convex lens is placed such that its focal point coincides with that of the first lens, the light emerging from the second lens becomes parallel again. This arrangement forms a telescope-type system.
The magnification of a telescope is given by:
\[ M = \frac{f_2}{f_1} \]
This magnification determines how much the diameter of the beam changes. If the second lens has larger focal length, the beam expands. If it has smaller focal length, the beam contracts.
This principle is widely used in laser optics where beam expanders are required to increase beam diameter while keeping rays parallel.
Important concepts involved:
• Ray optics and lens formula
• Telescope principle
• Angular magnification
• Collimated beam properties
• Optical instrument design
Common mistakes students make:
• Using lens formula unnecessarily.
• Confusing linear magnification with angular magnification.
• Forgetting that beam expander behaves like telescope.
In JEE Main and Advanced, telescope-based conceptual questions are frequently asked. Understanding relation between focal lengths and magnification is extremely important.
1. What is a collimated beam?
It is a beam of parallel rays.
2. Why use two convex lenses?
To expand or compress beam diameter while keeping rays parallel.
3. What is telescope magnification formula?
\(M = f_2/f_1\)
4. Does lens formula apply here?
No, because object is at infinity.
5. Why does diameter ratio equal focal length ratio?
Because system behaves like telescope.
6. Is this important for JEE Main?
Yes, ray optics questions are frequent.
7. What happens if f2 < f1?
Beam contracts.
8. What if lenses are not separated by f1+f2?
Output will not be collimated.
9. Is this concept used in lasers?
Yes, beam expanders are used in laser optics.
10. Which chapter covers this?
Ray Optics and Optical Instruments.
This content is created strictly for educational and competitive examination preparation purposes only. It is not affiliated with NTA or any official examination authority.