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

In solving this problem, we need to determine the power of a combination of four convex lenses and the total magnification compared to one lens. Here’s the step-by-step explanation:

Power of the combination: For lenses in contact, the total power \(P_{\text{total}}\) is the sum of the individual powers. Given four identical lenses, each with power \(p\), the total power is:

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

Total Magnification: Magnification of a lens depends on its focal length, which is inversely proportional to its power. The combined magnification \(M_{\text{total}}\) of four identical lenses in series is the product of the magnifications of each lens. If the magnification of one lens is \(m\), then for four lenses:

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

Conclusion: The power of the combination is \(4p\) and the total magnification is \(m^4\). Therefore, the correct answer is \(4p\) and \(m^4\).