the power of combination of two lenses x and y is 4d if the focal lenght of the lens is 12.
Calculate the focal lenght of lens y.
Determine the nature of lens y.

Dear Student,
Given
The power of combination of two lenses x and y is 4 d.
The focal length of the lens x is f_x = 12 cm (assuming it to be cm as the unit is not provided.)
Let the focal length of the lens y be f_y.
$$\begin{gathered} P=\frac{1}{f_x}+\frac{1}{f_y}=4 \\ \frac{1}{0.12}+\frac{1}{f_y}=4 \\ \frac{1}{f_y}=4-\frac{100}{12}=\frac{48-100}{12} \\ {f}_y=\frac{12}{52}=-0.231 m=-23.1 cm \end{gathered}$$
Since, the focal length is negative, the lens mut be diverging in nature. Thus, the lens y is a concave lens.

Regards