Question: 13. 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-
(1) 4 p and 4 m
(2) p^{4} and 4 m
(3) 4 p and m^{4}
(4) p^{4} and m^{4}
Answer: Option (3)
Explanation:
For thin lenses placed in contact, the effective power of the combination equals the algebraic sum of individual powers. If each lens has power p and there are four identical lenses in contact, the total power P_{\text{total}} is
P_{\text{total}}=p+p+p+p=4p.For magnification, when lenses are used in succession and are in contact (so image formed by one lens acts as object for the next with negligible separation), the overall lateral magnification is the product of individual magnifications. If each lens produces magnification m, then the total magnification M_{\text{total}} is
M_{\text{total}}=m\times m\times m\times m=m^{4}.Therefore the combination has power 4p and total magnification m^{4}, which corresponds to Option (3).