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 the power (p) and magnification (m) for each lens will be, respectively

The correct answer is 4p and m⁴.

Let us analyze the combination of thin convex lenses in contact step-by-step:

1. Power of the Combination:
When two or more thin lenses are placed axially in contact with each other, the total power of the combination ($P_{\text{total}}$) is the algebraic sum of the individual powers of the lenses.
Here, we have four identical convex lenses, each having a power of $p$.
Therefore, the power of the combination is:
$P_{\text{total}}=p+p+p+p=4p$

2. Total Magnification of the Combination:
When lenses are placed in contact (or arranged in a system where the image formed by one lens acts as the object for the next), the total magnification ($M_{\text{total}}$) of the lens combination is the product of the individual magnifications of each lens.
Here, each lens has a magnification of $m$.
Therefore, the total magnification is:
$M_{\text{total}}=m\times m\times m\times m=m^4$

Thus, the power of the combination and the total magnification are 4p and m⁴, respectively.