The following figure represents two biconvex lenses \( L_1 \) and \( L_2 \) having focal lengths 10 cm and 15 cm, respectively. The distance between \( L_1 \) and \( L_2 \) is:
- 10 cm
- 15 cm
- 25 cm
- 35 cm
The Correct Option is C
Approach Solution - 1
To solve the problem of finding the distance between two biconvex lenses \( L_1 \) and \( L_2 \), we need to apply the concept of lens combinations. The given lenses have focal lengths \( f_1 = 10 \, \text{cm} \) and \( f_2 = 15 \, \text{cm} \).
The image formed by the first lens \( L_1 \) acts as the object for the second lens \( L_2 \). For lenses in contact or separated by some distance, the effective focal length \( F \) is determined by placing the lenses close enough so they affect each other.
The distance between the lenses can be computed using properties of lens systems. Although the exact derivation depends on system specifics, options suggest distances based on common setups in optical configurations. Here, common practical arrangements in such setups have been considered, usually summing or making the focal conditions for minimal distance:
- The correct distance is given as \( 25 \, \text{cm} \). This value likely represents an effective point where the radii of curvature and physical separation create a compounded focal situation typical in practical lens applications.
- Other distances like \( 10 \, \text{cm} \) or \( 15 \, \text{cm} \) directly match individual lens' focal criteria, and \( 35 \, \text{cm} \) often exceeds practical design separations creating dilutive focal strength without special considerations.
Therefore, given options informed by typical configuration scenarios, the distance between \( L_1 \) and \( L_2 \) is 25 cm.
Approach Solution -2
The distance between two lenses, when both lenses are separated by a distance \( D \), depends on their focal lengths and how they interact. For this setup with two biconvex lenses, the total distance between them \( D \) is the sum of their individual focal lengths:
\[ D = f_1 + f_2 = 10 \, \text{cm} + 15 \, \text{cm} = 25 \, \text{cm}. \]
This configuration ensures that parallel rays entering the system pass through the first lens's focus and exit the second lens as parallel rays, which is a key condition for this lens arrangement.
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