Question

In a certain camera, a combination of four similar thin convex lenses are arranged axially in contact. Then the power of the combination and the total magnification in comparison to one lens will be, respectively:

• A. \( 4p \) and \( m^4 \)
• B. \( p \) and \( 4m \)
• C. \( p \) and \( m^4 \)
• D. \( 4p \) and \( 4m \)

Hint:

For lenses in contact, powers add up (\(P_{eq} = \sum P_i\)), and total magnification is the product of individual magnifications (\(M = \prod m_i\)).

Answer 1

The Correct Option is A

To address this problem, we must calculate the combined power of four convex lenses and their total magnification relative to a single lens. The process is as follows:

Combined Power: When lenses are in direct contact, their total power \(P_{\text{total}}\) equals the sum of their individual powers. For four identical lenses, each with power \(p\), the total power is calculated as:

\[P_{\text{total}} = 4p\]

Total Magnification: A lens's magnification is determined by its focal length, which is inversely proportional to its power. The combined magnification \(M_{\text{total}}\) of four identical lenses arranged in series is the product of their individual magnifications. If one lens has a magnification of \(m\), then for four lenses:

\[M_{\text{total}} = m \times m \times m \times m = m^4\]

Summary: The combined power of the lenses is \(4p\), and their total magnification is \(m^4\). Consequently, the definitive answer is \(4p\) for power and \(m^4\) for magnification.